Chrissyg, the press are reporting the figures that EODY, the official Greek health body are telling them. As Ros21m pointed out, EODY reported that 509 new cases were recorded between 1 to 15 July and 278 were imported by travellers. These are the "hundreds" that you saw reported in the press. They are not figures made up by the press. They are official figures. Clearly they are not from the UK since direct UK flights only got going on 15 July.
It is not nonsense that the government is keeping the closure of borders under review. The government has openly stated that if the number of new daily cases rises above 50 they will need to consider
reversing the opening up to tourist measures. Note the word "consider". So far they have only shut down specific border crossings where the incidence of imported cases was high. It is pretty clear if testing of UK arrivals reveals very low numbers of infections then UK flights will still come but if testing reveals large numbers they will stop. The same is true for any other country. It is common sense.
The following new cases were reported since UK arrivals started:
15 July 27 cases
16 July 29 cases
17 July 25 cases
I do not know of any report that says these cases are due to UK flights. If you believe you read that then please link your source. They are simply the number recorded on those days, some from travellers and some by internal infections. The number of new cases per day has steadily increased since 1 July and has even been as high as 60 on a single day. I think the steady rise is more worrying than the odd single day spike. Nobody is attributing this to the UK.