The public weather forecast is quite confident that there will be thunderstorms and associated low visibility / precipitation events coming up from the continent on Thursday around mid-day. There does not seem to be any issue about the necessary airmass with hot and humid air to do this coming up, rather the timing and path it will take when it goes over the South East.
So, if you have a flight on Thursday mid morning to late evening from LGW or LHR on BA...you may want to watch the forecast closely both tomorrow and Thursday to see how this develops and remember that at least LHR is at capacity so any thunderstorms are going to mess up the schedules...
Not trying to scaremonger, hoping rather to inform and suggest you watch the situation and be flexible to deal with any delays or cancellations of short haul...which usually come with this type of weather.
I'll try to update the thread with TAF forecasts when they apply to the period but this won't be until tomorrow really (UK time). The current TAF only runs until midnight of Wed/Thurs, so we really need to wait for the 13:00 issue of the TAF tomorrow to see how the forecasters are thinking things will develop.
I hope the weather tracks elsewhere and I end up looking an @ss...but just in case.
Safe travels.
You can see the current public forecast via the BBC here:
http://www.bbc.co.uk/weather/
using the video embedded in the page on the right hand side.