My first piece of advice would be to get the test in advance, read the instructions fully (in my case several times!) and take your time.
This company, Eurofins, are by far the cheapest that I've found:
Their 'Test to Depart' is £44.90 and their 'Test to Release' is the same and they're government approved.
They have drop off points around the country or you could possibly take the test to the post office and have it upgraded to signed for or special delivery.
I also used BioGrad on my last return to the UK for Day 2 and 8 (postal) testing. I also used them for Test to Release on Day Five (I went to their clinic near Manchester Airport for that). In all cases I got my results within 24 hours.
I used Medicspot when I flew (also government approved). Much more expensive (I didn't know about Eurofin!) at £149 but I went and collected my test, did it in the car and gave it back to them. They have couriers collecting every day (that the individual pharmacies are open) and seem to have a bigger network of places to collect from. They are offering 10% off testing with the code below but that's still considerably more than Eurofins. I suppose it'll depend on whether it's important to you to be able to drop the test off etc. (I get a £10 Amazon voucher, incidentally for each test booked with Medicspot, but would still suggest Eurofins - so much cheaper!).
Here's the Medicspot link and discount.
BE WARNED: Whichever service you use, check the time that the courier is expected... The pharmacy I chose closed at 1pm and I got there at 12pm thinking I had plenty of time, only to hear that the courier was expected at 12.30pm! If I'd left it to the last minute I'd have been scuppered...
There are plenty of other companies out there offering test but Eurofins is the cheapest I've found and Medicspot and BioGrad are the only ones I've had direct experience of.
WHEN IN GREECE
It's very easy to get a Rapid Test or PCR booked in Greece. The Rapid Test costs 30 euros and the PCR is 60 euros, plus the taxi cost to Nidri and back (it's normally shared or we can arrange a minibus if there are sufficient numbers) so would be between 5 and 10 euros per person).
Or arrange to take a test with you. A number of our June guests used Qured which costs £39 and can be done at your accommodation in Greece with a health adviser monitoring (to make sure it's you who takes the test and that it's your result!).