He indicated the prime minister will not be taking part in the new scheme inviting people fleeing the conflict in eastern Europe into their homes, but said it was up to individual ministers what they decide to do.

Transport Secretary Grant Shapps said his family will be applying for the programme, and the Levelling Up, Housing and Communities Secretary Michael Gove said he is considering putting himself forward as a host.

However, Health Secretary Sajid Javid said it would be difficult for him to "offer the time" and Labour's London mayor Sadiq Khan said he does not have the space in his family home.

Kyiv 'like apocalypse movie' today - latest Ukraine updates

Mr Johnson lives in the flat above 11 Downing Street with his wife Carrie and their two children.

The PM's spokesman said: "There are specific challenges around security on housing people in No 10.

"Various ministers have been asked about this. Obviously it will come down to individual circumstances. This is a significant commitment."

The scheme will see households paid a tax-free £350 a month as a thank you for hosting a refugee for a minimum of six months.

There will be no limit to the number of Ukrainian refugees who can come to the UK as they face their "hour of greatest need", Mr Gove told MPs.

Read more: How will the scheme work?

As an immediate step, those wishing to make such an offer are being asked to register their interest on the new "Homes for Ukraine" website.

Mr Gove said the scheme would be based on "the enormous goodwill and generosity of the British public and our proud history of supporting the vulnerable in their hour of greatest need".

Government sources later said, as of 6.30pm on Monday, 20,000 people had already signed up to offer their homes to Ukrainians.

This included 1,500 people registering to offer support within the first hour of the website going live on Monday afternoon.

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Mr Javid said if people do not have the capacity to offer space in their homes, there are other ways to help.

He told LBC: "It's important that anyone that becomes a host, that they can fulfil the obligations of a host, that they can spend time with these families but there are many ways that we can all help and whatever I do at a personal level, I will most certainly be helping."

The health secretary said he has donated to the Disasters Emergency Committee appeal for Ukraine.

Mr Shapps, meanwhile, has announced his personal support for the hosting scheme.

He tweeted: "We've spent the past few weeks as a family discussing the devastating situation in Ukraine and so we intend to apply today to join other UK households in offering our home to provide refuge to Ukrainians until it is safe for them to return to their country."

On Sunday, Mr Gove said there are potentially "hundreds of thousands of people" in the UK willing to take Ukrainians into their homes.