There's no reason why it shouldn't work.
There's no such a thing really as fit to fly test, you just need a negative test result (PCR/Antigen) and you're fit to fly, and that you get from the day 2 test.
In UK the only tests that you can't use for travel is a free test provided by the NHS.
Just make sure that your test is taken on a day that you should be able to use it as pre departure test, as some countries require from UK a test taken up to 24 hours before departure.
See uk government foreign travel advice where you'll find information on all tests you'll need when you travel from the UK.