As a former Ukrainian citizen, my citizenship was revoked automatically as soon as I received my British citizenship.
That’s not true. Ukraine does not revoke citizenship automatically.
You should request for renouncing of your Ukrainian citizenship in the Embassy of Ukraine in the UK.
If you did not request it, then you are treated as a citizen of Ukraine.
Keep in mind that the Brexit situation is still extremely unsettled as of today (March 23th 2019) and that a “hard Brexit” remains a possibility.
While both sides proclaim that there will be generous solutions for UK and EU27 citizens, you should expect that exceptions and special cases may disappear. A proper passport is a good idea.
As Ukraine is not in the EU https://www.gov.uk/eu-eea according to Timatic you need a passport to enter https://www.timaticweb2.com/integration/external?ref=d975cfc59f5c0abd06d16e872198110b&clear=true
BRPs must be returned to the Home Office within 5 working days of getting your certificate of British citizenship, you can be fined up to £1,000 for not doing so. You cannot enter the UK using your BRP or certificate of British citizenship. https://www.gov.uk/apply-citizenship-indefinite-leave-to-remain/after-you-get-your-certificate
Don’t forget that you must return your BRP after naturalisation. It’s no longer valid and you must not use it.
For international travel you will need a valid travel document. Also please be aware that the UK typically wants UK nationals to use a UK passport when they enter the country.
Credit:stackoverflow.com‘