Ahh - yeah, these were built when nukes still had relatively low yields. Soon enough it became clear that they wouldn't withstand a ground burst from a big nasty ICBM. Therefore they built a huge bunker outside Bath called RAF Corsham where the central Government could run the country from. It's still an active MOD site - although it's been mothballed.
There are other smaller bunkers around the country for regional seats of government (SRHQ's) - preserved ones include Hack Green, Kelvedon Hatch and Anstruther.