Day 2 vs. Fit to Fly tests UK

I am currently planning a short trip to the UK. I'll head on to another destination afterwards.

I am fully vaccinated, so to enter the UK I understand I will need a lateral flow test followed by a PCR test on arrival/up to day 2. My onwards travel requires a PCR fit-to-fly test.

Is there any way to get this done in the UK with only one PCR test when the timing of the day 2 PCR is right for the final destination fit-to-fly certification? All the labs I have looked at seem to offer PCR tests either as fit-to-fly tests or as day 2 arrivals tests and seem to suggest that it is not possible to use a fit-to-fly certificate for day 2 or the other way around. This makes me think that the day 2 PCR will not come with a certificate that is suitable for onwards travel. On the other hand, it seems very wasteful (and expensive) to run two tests that are bound to have the exact same result unless some laboratory error happens.

I would be especially interested in whether a simultaneous day 2/fit-to-fly test is possible somewhere near Heathrow airport, but any information on this would be very useful.