As mentioned above, unless you happen to be in an area which has separate cable service or similar, BT still owns the physical lines from the house back to the exchange. In many parts of the country, BT is still the only company providing this local loop, so even if you transfer or get new service with some other company, it will still be BT which connects up the actual wiring to your home.
The issue of just how much work is involved in re-connecting a line which has been out of service for a while is a tricky one, because it all depends on the situation. When somebody moves out and discontinues service, the line will just be marked as spare at the exchange. It's all computerized these days, of course, so a few software commands will immediately render the line inoperable for both incoming and outgoing calls.
If you move in fairly soon afterward and the line is still physically connected, then all it takes is some more programming to set up your new number and associate it with the physical pair of wires. However any spare pairs in the large cables which run out to various neighborhoods are considered fair game for reallocation when needed. So the longer that line sits unused, the greater the chance that at some point it will be disconnected from the exchange so that the pair of wires it used previously can be allocated to somebody else. The wires will still be there from the house to the nearest distribution point (either atop a pole or in a street-corner cabinet), but that might be as far as they go. Re-establishing service in this case obivously involves more work to physically reconnect your line to the exchange again. In some places where there is a shortage of lines, it could also mean installing pair-gain units, which allow two subscribers to share one pair of lines (kind of like an old-time party line, except that in this modern version you can both use the phone at the same time and neither party is actually aware that the line is shared).
Unfortunately, it would be very complex to base the charge on the amount of work involved, not to mention confusing to the general public ("How come my friend's new line only cost £25 but mine was £200?"), so BT applies the standard installation charge to all situations.