Police were called on Monday over concerns for three people who had not been seen for several days.
Officers forced entry into a property in Great Denham, where they found the bodies of a woman and two children, Bedfordshire Police said.
Police said they have identified a suspect, who was known to all three victims, and who they believe has since left the country.
Investigators fear the three alleged victims could have been murdered.
Official identification of the woman and both children have not yet taken place, the force added.
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Assistant Chief Constable John Murphy called it an "incredibly complex investigation" and said: "This is a deeply distressing incident in which a mother and her two children are believed to have been murdered.
"Our thoughts are first and foremost with all those affected.
"We recognise that this will cause concern in the local community and beyond."
He urged anyone with information about the incident to come forward.
ACC Murphy added: "While there is nothing to suggest there is any wider risk to the public, we will be increasing the police presence in and around the area to support the investigation and provide reassurance to residents."
The far-right leader was found guilty of misappropriating public funds by a court last March.
Her political future had been on the line today as a Paris appeals court ruled on her eligibility for the next election.
She received a five-year ban from public office in March 2025 for embezzling more than €4m (£3.4m) from the European Parliament.
Judges upheld the earlier court judgement that she was guilty of misappropriating EU funds and ruled she is ineligible to hold public office for 45 months, but suspended this for 30 months.
While that ruling clears the way for Le Pen to run in the 2027 presidential election, the court also sentenced her to a three-year jail term: two suspended and one with an electronic ankle tag.
So while it will not prevent her from entering the race for France's highest office, it would make any campaign politically and logistically difficult.
Le Pen left the courtroom without speaking to journalists and her lawyers said she would reflect upon the verdict.
She has previously said she would be reluctant to campaign for the presidency while serving a sentence under electronic monitoring.
On Tuesday, Health Secretary James Murray took questions from birth trauma survivors and bereaved mothers wanting to know how he intends to address shortfalls in the system.
The queries were put to the health secretary by Sky News' Sophy Ridge as part of a special programme on the Mornings show, which she hosts alongside Wilfred Frost.
It comes as Sky News has spent months highlighting the flaws and issues across the UK's maternity care system.
After the health secretary replied to the questions put to him on maternity services, women on the panel who had been listening in were unimpressed.
Rachel Coles, birth trauma survivor, said: "We've had review after review after review, and we've heard things just said like 'oh yeah, we'll be looking at that, we'll be doing that'... when?
"Because people are dying, women and babies are dying.
"And there comes a point when you actually have to step up and step in and they're not doing it."
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Another survivor wondered how it took so little for the government to green-light the opening of pubs until 5am on Monday to watch England play against Mexico in the World Cup, but action on maternity care keeps dragging.
"I just think there is just such blatant misogyny rife within government and obviously within healthcare from kind of what we're talking about," Hannah Swinburn said.
"Women have been screaming and shouting for years that they just want safer, respectful maternity care. And yet we can't pass legislation for that."
She added: "I don't understand what's just taking so long. If this is a priority, make it a priority."
Birth trauma survivor Neya Joshi asked the health secretary how the government would seek to improve post-natal care in hospital.
The health secretary replied: "There are some things that I'm prioritising right now as things we can do straight away. But I know that that's not the answer.
"I know that the answer has to be comprehensive, to take every aspect of maternity services and every part of women's interaction with maternity services from beginning to end."
Asked about his reply, Ms Joshi said she didn't really feel like Mr Murray had answered her question.
"I think staff accountability is really important because if you don't have that, then the same behaviours are going to be repeated," Ms Joshi said.
"Women are literally getting traumatised from the way that they're being spoken to, not just on postnatal wards, but generally as well."
Mr Murray was also asked if a public inquiry was being considered.
He replied an inquiry was "not off the table", but added it would be helpful to have a Hillsborough Law in place, forcing a duty of candour on public servants who could face jail if they don't answer questions honestly.
"In Nottingham, Donna Ockenden's review there, senior leaders in the local NHS refused to take part in her review," Mr Murray said.
"I think that's completely unacceptable, it feels wrong. I cannot understand how they, on a personal level, take that decision not to be part of it.
"So that's why the duty of candour that I mentioned means that in future in Leeds and Sussex, when the reviews are taking place there, senior leadership in the NHS won't be able to refuse; if they do, up to two years in prison is the ultimate sanction.
"They will have to take part because no one should be able to avoid that accountability."
Interpol put out an alert after Vadym Iermolaiev was said to have been targeted in a blast in Monaco last week.
The attack injured three people and sparked a manhunt across multiple countries.
Anastasiia Berezovska, a 39-year-old from Ukraine, was named as the suspect in an Interpol red notice but has now been found dead in Ukraine, the country's security service (SBU) has said.
In a lengthy statement, the SBU outlined what appears to be a complex and convoluted investigation, involving a serving intelligence officer and cryptocurrency wallets.
Sky News has been unable to independently verify the account as outlined by the SBU.
The security service says it was able to establish who Berezovska had been in contact with and traced her movements, which showed she arrived in Ukraine on 1 July.
Contacts included members of her family and two men - the first a former law enforcement officer and the second a serving officer in Ukraine's military intelligence agency (HUR).
The SBU said it has information that both men repeatedly transferred money to Berezovska's cryptocurrency wallets and bank accounts, possibly implicating them as accomplices in the attempted murder in Monaco.
Urgent investigative actions and searches were carried out, the security service added.
The SBU said that, during these investigations, the serving HUR officer stated that he had killed Berezovska together with the other suspect.
He also said that he had not informed his superiors about his contacts with Berezovska, the money transfers to her, or any of his other actions, and that he had acted on his own initiative, the SBU alleged.
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During a search of the former law enforcement officer's residence, investigators also discovered a basement that resembled a torture chamber, the SBU claimed.
Both suspects have been detained on suspicion of committing murder by prior conspiracy as a group.
Berezovska's body was found with gunshot wounds to the head along with spent pistol cartridge cases.
Rescuers were deployed to the scene in Gansu province at 7am local time on Tuesday, where 33 people were initially trapped in a valley in Tanchang county.
They had found 21 people by the afternoon, but five subsequently died despite receiving emergency treatment.
Most of those affected were residents from nearby villages hired as temporary workers at a state-run forestry farm.
Local authorities have relocated other residents as they continue the rescue operation.
The cause of the landslide has yet to be determined, but the mountainous region is prone to natural disasters - particularly during the rainy season.
A disastrous 2008 earthquake in the neighbouring Sichuan province killed over 69,000 people, and partly destabilised geological conditions in the region.
More landslides have also been recorded in the region in recent years.
In August 2020, mudslides killed at least five people and displaced more than 72,000.
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In 2010, another mudslide in Zhouqu County killed over 1,500 people, with more than 200 left unaccounted for.
Chinese President Xi Jinping has demanded comprehensive rescue efforts following a number of devastating weather events in recent days, including tornadoes and landslides.
China's state planner has also announced 30 million yuan (£3.29m) in relief funds for the region.