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