I do have UK and EU passports. Going to Turkey is fine. I found this at
Coronavirus (COVID-19): jobs that qualify for travel exemptions - GOV.UK (www.gov.uk)
Transiting airside through the UK
Applies to:
People transiting airside (individuals who arrive in the UK but do not pass border control).
You will need to
complete the passenger locator form before you travel to the UK.
You will not need to self-isolate as you are only transiting via the UK.
You will not need to show anything as you will not pass through the UK border.