Designated countries
The UK has driving licence agreements with a variety of ‘designated countries’. If you hold a driving licence from one of the countries below, you'll be allowed to exchange it for a UK driving licence without taking any further tests.
Andorra, Australia, Barbados, British Virgin Islands, Canada, Cayman Islands, Falkland Islands, Faroe Islands, Gibraltar, Hong Kong, Japan, Monaco, New Zealand, Republic of Korea, Republic of North Macedonia, Singapore, South Africa, Switzerland, Taiwan, Ukraine, United Arab Emirates, and Zimbabwe
If you hold a driving licence from a designated country, you'll be allowed to drive in Great Britain for up to 12 months. Once this time has passed, you will have to exchange your licence. You've got 5 years from the day you became a resident to exchange your licence—as long as it's still valid.
https://www.gov.uk/exchange-foreign-driving-licence
There is a designated person for Ukrainians at DVLA to send documents to:
Lee Jones UA, DVLA, Swansea SA6 7JL
The cost to exchange licences is £43 plus postage (you are advised to send prepaid secure/tracked envelopes to have your ID documents returned).
Worth thinking about:
There do seem to be issues that the Ukrainian Driving License doesn’t say whether it is for a manual or an automatic vehicle. The experience is that DVLA will only issue a license for an automatic car - please check this out.
The other issue is that when you exchange your license you have to send in your Ukrainian license and therefore lose it!
A number of Ukrainians we have spoken to have decided to keep their Ukrainian license and go through the UK Driving Test process.