There are no caves in Reading.
The chalk mines:
One entrance is on private land and is well fortified as it would be a long open drop in the middle of housing estate otherwise.
The other entrances are gated for the same reason and I am not sure if they are still openable.
There are probably lots more entrances but as most were closed before 1900 they did not have to be marked. Some house owners are discovering them and wish they hadn't.