I've no doubt that both the May temperature records (highest max and highest min) and overall records will be broken again, but for an equivilent 'sudden' rise, we'd be looking at 37.4c for May, and 41.9c for Overall records. Even with climate change, the records can't rise as fast forever. Eventually you run out of perfect setups, and rely on climate change nudging up the maximum potential slightly. We haven't had 2c of warming in the last 75 years, so this recent May record had to have had more perfect condtions for a record than the 32.8 previous one, even with climate change added into the mix.

If you look at the Met Office's "Download Regional Values" of Max T for S E & S England since 1960 we have, in fact, had well over 2C of warming due to Climate Change in that period. So if the existing record is quite an old one as it was for May then a sudden jump of 2 to 3C for the record where perfect conditions have just been hit again is not that unreasonable. It just comes as a shock to the system when it occurs !

https://www.metoffice.gov.uk/research/climate/maps-and-data/uk-and-regional-series 

The June record could be broken by 4 or even 5 degrees if the models are correct.

I can't see the July record being broken by that margin any time soon though. 45C in the UK is really pushing the realms of possibility.

The May and June records were/are both quite old - June being the more recent at 1976 - in that time we have experienced a general increase of summer max of over 2C so it is not beyond the bounds of possibility that given ideal conditions these older records can be smashed by some distance as already happened in May this year

The July record, however, is much more recent at 2022 so it would be astounding to see this one beaten by a similar amount just 4 years later. Similar logic can be applied to the August record from 2003