I turned on the hall lights today and one of the bulbs blew (the only
remaining one that worked in fact). There was quite a bang and now I find
that replacing the bulb does no good.

It is likely that the current surge from the blowing incandescent light has
burned away a bad connection that already existed in the wiring. Quite
frankly, that and the mention of rewirable fuses strongly suggests that you
should get an electrician round to do a full periodic inspection. Unless a
junction box has been buried somewhere, it is likely that this survey will
indicate the location of the failed connection.

I unscrewed the two hall lights and all the wires seem intact, ditto the
switch.

The failed joint could be on any of the failed lights, or any of the other
lights on the same circuit that is providing the feed. It could also be on a
crimped connection or junction box buried somewhere.

Christian.