The UK has been widely criticised for not allowing as many Ukrainian refugees to enter as some other European states.
What are the schemes?
Family visa scheme
The family visa scheme is for Ukrainians with a family member in the UK.
That family member must have British nationality, indefinite leave to remain, settled status or proof of permanent residence.
It was launched at the beginning of March, and extended after criticism that it excluded some close family members.
Ukrainian refugees are advised to apply at a Visa Application Centre (VAC) in countries including Poland, Romania, Hungary and Moldova. They need to provide biometric information, such as fingerprints.
Applications from refugees with a Ukrainian passport can be made online, with biometric information provided after arrival in the UK.
As of 7 April, the UK had issued 28,500 visas under this scheme from 36,300 applications. However, only 10,800 have arrived in the UK under this scheme so far.
The "Homes for Ukraine" scheme lets people in the UK host Ukrainians refugees who are known to them, but who do not have family ties here.
It was launched on 14 March, and more than 100,000 people and organisations signed up within the first day.
Under the scheme, people are asked to offer Ukrainians a rent-free space in their home or a separate residence for at least six months. They will not be expected to provide food and living expenses but can choose to do so.
Those offering to host a refugee will be vetted by the government and Ukrainian applicants will undergo security checks.
Each household housing a refugee will be offered £350 a month, tax-free, for up to 12 months.
Local authorities will also receive £10,500 in extra funding per refugee for support services, with more for children of school age.
However, some families who have applied to be sponsors have complained that the system is overly complicated.
Government figures show that as of 7 April, 12,500 sponsorship visas had been issued from 43,600 applications. However, only 1,200 refugees have arrived in the UK so far under the sponsorship visas.
Why has the UK government's response been criticised?
The Home Office has been accused of a chaotic and overly-bureaucratic response.
EU countries are allowing Ukrainian refugees in for up to three years without a visa, and more than four million people have fled to neighbouring countries since the Russian invasion.
Poland has taken more than 2.5 million refugees, and Romania more than 650,000. As of 7 April, 40,900 UK visas had been issued in total, but only 12,000 have reached the UK so far.
On 8 April, Home Secretary Priti Patel apologised "with frustration" for visa delays.
On 26 February, Home Office minister Kevin Foster was widely criticised after highlighting the government's Seasonal Worker visa, which allows people to apply to come to the UK to pick fruit and vegetables.
His tweet was subsequently deleted.
There have been complaints that the UK visa process is too complicated - one British man told the BBC it had taken 72 hours to get a visa for his Ukrainian step-daughter, who had fled to Romania.
There have also been reports of refugees who have got as far as Calais, before being turned away by Border Force officials for not having the right paperwork.
On 7 March, Home Secretary Priti Patel told MPs "we have set up a bespoke VAC en route to Calais". But the Home Office did not confirm that this was the case.
The government then opened a VAC in Lille on 10 March - around 70 miles away from Calais.
The Home Office said it would deal with "a limited number of cases" - referred to it by Border Force officials - and advised applicants not to travel there.
Why have so few visas been issued by the government so far?
- a visit from local authorities to ensure that properties are fit for purpose
- basic DBS check if hosts are sponsoring adults
- enhanced DBS check if hosts are sponsoring children under 18 or vulnerable adults.
It is likely that the vetting process will exacerbate what already seems to be a long and complex visa application process.
Will the UK lift visa rules for Ukrainian refugees?
The government has faced pressure - including from some Conservative MPs - to issue emergency visas or lift visa requirements altogether for Ukrainian refugees.
Home Secretary Priti Patel has ruled this out, insisting that "security and biometric checks" were vital to keep British citizens safe.
The government also says that some people in Calais claiming to be Ukrainians have presented false documents.
Boris Johnson has defended the current visa rules, saying: "People want us to be generous but also careful."
He has also repeatedly talked about the government's "proud record" on refugees since 2015, telling MPs "we've done more to resettle vulnerable people than any other European country since 2015".
However, this only refers to one specific category - "resettled refugees". Other European countries have taken in larger numbers of refugees in general.