It would start out as being tax resident in both. Tax resident in UK by being incorporated there and tax resident in Cyprus by being managed there. However, then you'll have to leverage the tax treaty to determine if you can get the company to qualify as treaty non-resident in UK making it tax resident only in Cyprus.
To what degree this is possible depends on the nature and structure of your business. Read up on the relevant agreements and have a chat with a tax adviser about that.
At the end of the day, it'd probably be a lot easier to just use a Cypriot company unless there's some reason you absolutely have to have a UK company.