This happened when I was at Battersea yesterday. Luckily in a twin so could depart via the LFA even though that's was the direction of the bad weather!! What would a single engined machine have done. Landed at Battersea then couldn't leave. The tower only got 10mins notice of the closure!!
I then couldn't understand why City couldn't give me a VFR transit north across their airspace (Class D) stating that no VFR transits because SVFR was closed. Interesting to see what will happen when it all goes Class D....