A survey of more than 1,000 Ukrainians finds the number in work and with bank accounts has increased.
About four in 10 Ukrainian refugees in the UK are now working, the Office for National Statistics (ONS) has said.
The proportion of Ukrainian nationals employed in the UK has risen from 9% in April to 42% at the start of August.
The findings come from a follow-up survey by the ONS of 1,132 Ukrainians, conducted between 20 July and 4 August.
More than 100,000 people from Ukraine have arrived in the UK under two visa schemes launched following Russia’s invasion.
The newly-published UK Humanitarian Response Insight Follow-up Survey (UKHRIS), was commissioned to “understand the opinions and experiences” of people arriving in the UK under both the Ukraine Family and Ukraine Sponsorship schemes.
The family scheme allows Ukrainian nationals and their relatives to join other family members already living in the UK, while the sponsorship scheme allows Ukrainian nationals and their relatives to come to the UK if they have a sponsor who can provide accommodation.
Two MPs, Victoria Prentis and Duncan Baker, have said they will continue hosting Ukrainian families in their own homes beyond the minimum six-month period expected under the Ukraine Sponsorship scheme.
Refugees who secure visas are allowed to stay in the UK for up to three years, and once in the UK, Ukrainians have the right to work, to access benefits, education and healthcare.
But while many have been successful in finding jobs, almost half of the people taking part in the survey said they faced barriers to their ability to take up work, including their English language skills.
Stories of people struggling to obtain safeguarding checks for certain jobs have also arisen.
Former MP Edwina Currie previously told the BBC a Ukrainian woman she was hosting in her home could not be considered for a job at her children’s school as employers could not check her Disclosure and Barring Service (DBS) status.
The first UKHRIS in April sampled 3,412 individuals, with the majority entering the UK under the Ukraine Family Scheme.
The recent survey followed up on 1,132 individuals and found the proportion of Ukrainian nationals with bank accounts was up from 43% in April to 93% in August.
The survey also found 93% of Ukrainian nationals who had completed the first survey had remained in the country, though most respondents said they did not understand how to apply to extend or change their visa, or what state benefits they may be eligible for.
Some 37% of respondents said they had enough money to support themselves for the next three months, up from 26% in April.
The findings of the latest survey come six months after Russia’s invasion began and in the same week outgoing prime minister Boris Johnson visited Kyiv to mark Ukraine’s independence from the Soviet Union 31 years ago.