Don't know about the UK but when I lived in Singapore I was on a flight which was diverted to Johor Baru airport in Malaysia because of ****e weather over Changi which stubbornly refused to budge.
I only had hand baggage and they put steps up to the plane so I asked if I could get off. They let me off, I went through immigration (who were quite surprised to see me) and got a cab over the Causeway back home.
Much quicker than hanging around in JB (sic)!