Any currency you bring to the UK you will have to change. The only currency accepted in the UK is British pound. You can exchange currency in your bank, when you open an account, or currency exchange office. Airports have very high exchange rates, so don't bother. In case of emergency, you can exchange currency in the souvenir shops on Oxford street in London, in John Lewis stores or in the stationery shop chain Ryman.
The best thing to bring is a Ukrainian bank card which you can use abroad. Use it to pay for goods and services here, until you open your own bank account and receive a UK bank card. Please be advised that Ukrainian banks have limits on currency withdrawal abroad. Inquire in your bank.
In the UK people barely use cash anymore even for small payments. Many places are now cashless.