There was a time when museums in this country were charging for the entrance, and even then Horniman museum was free. From what I heard at the time, the management of the museum could never charge an entrance fee, as this was a condition of the Horniman’s Trust which no one could get around even then. The trustees may face difficult time in running the museum if its funding gets cut, but 2015 is a bit far away in these challenging times and one would hope they would not immediately be looking at the closure.
As already mentioned cuts in social services are more imminent danger.