There is a very low chance of these CAPE/LI values. The models tend to downgrade the values on the day, as mentioned above, so it may well be less than a third of the forecasted values and much less widespread. A good example would be that storm earlier this month, in which an Estofex (L2) warning was issued for, and the storm occured on the opposite side of the warning zone. In addition to that the CAPE/LI values dropped immensely.
As for the heatwave, which may indeed trigger violent storms, Metcheck has stated:
"In all fairness, this is the first time the new GFS has had an opportunity to handle a proper Spanish plume and therefore many forecasters are a little hesitant to go with exactly what the GFS is saying, but the ECM is also showing a large area of very warm air spreading from from Spain and France from Wednesday onward next week."
"OK Metcheck, so it's a heatwave... what's new? Well, the GFS is suggesting maximum temperatures around the 35-37c (95-99f) mark on Thursday. The record for the UK in July is 36.5c and that could well be broken if the output is correct. Not just that, but the new GFS has been consistently under-estimating maximum temperatures recently."
It may be too short-lived to be a proper heatwave, but any heat at those temperatures with those CAPE/LI values would easily trigger a few violent storms. I am pretty gobsmacked that according to Netweather it may feel like over 40 degrees, but really it would be the storms that we want, the heat is just the trigger - but the risk of storms are actually low next week.