The Cheltenham Festival took place from 10 – 13 Mar 2020. 251,684 people attended the 4 day event. As you say, some would have been indoors, but a minority. The majority would have been outdoors. NHS Test and Trace was only launched at the end of May 2020. So any "investigations" into where people may have contracted the virus were being done at that point by the hospitals themselves when Covid patients were being admitted. My source for citing the 2020 Cheltenham races is a very high-up in Gloucestershire Public Health who is a friend and former neighbour and whom I have no reason to disbelieve. The common denominator in the majority of these cases was, reportedly, the race event (for Gloucestershire).
The odd thing is that the data recorded doesn't really support that conclusion. In a presentation given by the Director of Public Health in Gloucestershire in May 2020, the case numbers do not exhibit a spike attributable to the Festival and she stated that the results "broadly mirrored the national picture". She went on to show further data that also does not support the contention that Cheltenham suffered a spike because of the Festival. Death rates were not statistically different from comparable areas.
Edge Health - a startup private health company seems to be behind the claim there was an identifiable spike from an April 2020 study and I have already referred to that.
A week of full hotels, bars, betting shops, transport, restaurants etc even by a minority will have had a far greater effect on transmission. All the available medical evidence is that the chance of transmission outdoors is very much lower - one study gave a mean estimate of 18.7 times lower and confidently between 6 and 59 times lower. In fact, there is very little evidence at all of outdoor transmission of covid at all. To the extent that there was actually any spike of infection associated with Cheltenham - and evidence of that is thin, it is far more rational to attribute it to indoor infection in bars, hotels, betting shops etc. than to insist on something that the known data does not support. The medical evidence is that people catch it indoors. It's simply implausible that outdoor transmission caused any harm.