Well, we sometimes have to wait until well into May, but it does look like we could see the first of what I would call 'warm air' thunderstorms of the year across parts of the UK overnight tonight and into tomorrow.
Overnight tonight, models do indeed break out precip across south-eastern parts of England, thence advecting/developing it NW'wards into parts of central England and Wales. This appears to be in response to isentropic lifting of 850 hPa high WBPT air atop a relatively cool boundary layer, as the 850 flow increases overnight, and differential thermal advection, as the 850 WBPT increases below fairly cool upper air. Note that this means that we may not see much moving NW from the near continent this evening - rather, it should develop here. There is a reasonable chance of thunder with this too. Shear in the cloud layer is not too high - around 20-25 knots, with a little veering - thus, rotating updraughts seem unlikely, but any stronger cores could bring gusty winds and hail, perhaps to 15 mm diameter or so.
Tomorrow, this lot should have cleared away to the NW, with sunshine developing across southern and some central parts of England. Somewhat lower 850 WBPT air will move into parts of SE England and E Anglia later in the morning and through the afternoon, meaning storms are unlikely here, or at least, if any develop, they will soon have moved away to the WNW. Further west and north-west, there will still be a moist and unstable airmass in place at peak heating - any storms which initiate seem most likely to do so (in the absence of any larger scale low-level forcing mechanism) in regions of small-scale forcing, such as elevated heating over the likes of the North Downs around the Berks/Hants border, or the Berkshire Downs/Salisbury Plain, and then moving NW'wards - others may develop over the Chilterns. Deep layer shear will tend to increase through the afternoon as stronger 500 hPa flow begins to arrive, and will increase further into the evening, reaching around 40 knots. Low-level shear will also tend to increase in the early evening. Given the lack of a major boundary to initiate storms, any which do form could remain fairly discreet. Parts of central southern England, the Midlands, and east Wales have a chance of some severe weather, primarily in the form of strong winds (up to 60 mph) and hail (20-30 mm dia). However, there is also the chance of a tornado or two, especially towards early evening in parts of the Midlands and east Wales. The shear is certainly sufficient for organised multicell storms, and these could contain rotating updraughts/supercell type structures, augmenting the severe threat.