if I don't should I disconnect the floating earth?

Probably.

For the sockets I would take them out but they are the two hoover
points.

Disconnect the sockets. Use a suitable extension reel into a different
socket.

All this assumes, as you state, that a proper rewiring is imminent anyway.
Make sure the lighting circuit is on a 6A MCB or 5A fuse. The shameful
bodger who put the sockets on the circuit may have upped the fuse rating to
"wire" standard when the cleaner tripped the fuse.

Christian.