I flew but it was before there were any restrictions in UK regarding leaving or reentry so everything I required was for Indonesia. The Covid test and health letter were required by the airline to allow me to get on to go to Indonesia - may be the same with yours for Turkey. I took mine to airport day before but normally you just turn up with them when checking in and they clear you with other country immigration authorities first (doesn't take long).
Covid test had to have been done within a certain time before departure (for Indonesia was less than 7 days before arrival). Best place to check is here:
https://www.gov.uk/foreign-travel-advice/turkey/entry-requirements
Don't forget that you should also carry the following items with you in your hand baggage as they may be required as part of your immigration check in Turkey:
1) sperm sample (minimum 200ml so you might want to start collecting now)
2) stool sample (in clear plastic bag - minimum 4in long)
3) urine sample (no more than 1 litre and stored in a children's party balloon)