If I'm not mistaken, at one time, ALL lines were BT
At one time all lines were owned and run by Post Office Telephones (with the exception of the city of Hull, which through a quirk of history had its system owned by the city corporation). British Telecom was created in the early 1980s and the government gradually sold off the telephone network into private ownership, which is how BT came to own all the lines. Other companies (starting with Mercury Communications, later absorbed into Cable & Wireless) were then able to offer competing services,
Technically though, BT
still owns all the lines. All that happens if you need the physical line installed to your house is that your chosen provider sub-contracts that part of the work out to BT. If you notice engineers out and about working on telephone lines, you'll see that the vans now carry the BT OpenReach livery, which is a fairly new division created specifically to service the outside lines. They are supposed to provide facilities to all service providers on an equal basis.
I know this has caused considerable confusion to some people when they sign up to get a new line installed with Virgin, Talk Talk, etc. and then a BT OpenReach van and engineer show up at their door.
What happens at the telephone exchange depends upon whether LLU (local loop unbundling) is in place or not. Many exchanges is cities now have LLU, which means that one or more of the competing companies actually rents space in the building from BT to install their own equipment. If you have a line provided by one of those companies, then your line is jumpered directly to that company's equipment at the exchange. If you are served by an exchange with no LLU (the situation in most smaller towns and rural areas at the moment), then your line is still actually served by the BT equipment, with your provider paying the appropriate fees to BT.
As for the connection/re-connection fee, the amount of physical wiring work involved can vary from case to case. The fact that you still have telephone sockets and a line back to the pole in the street doesn't necessarily mean that you still have a circuit all the way back to the central office. It will depend upon how long (if it all) the line has been out of use, how much demand there has been for new phone service in your neighborhood, etc. If the line is still connected all the way back and there is no LLU at your exchange, then it will just be done by programming in the equipment. If the line is still connected to another company at an LLU exchange, then it will also need to be jumpered back to the BT equipment -- Not a big task.
However, if the line has been out of service for a while and pairs in the assorted cables back the office have been used for other circuits, reconnection could involve a visit to several distribution points along the route to reconnect your line all the way back to the central office. If there are no spare pairs available, it can involve the installation of extra equipment on the poles which will allow two lines to work over one pair of wires. Obviously in some cases providing a new line can also involve installing an extra pole or two to get the line to you (new house away from existing lines etc.).
Rather than try to price up each job individually, BT opted for a fixed connection fee set at an average level to keep things simple. £125 might seem like a lot to just run a jumper across a single distribution frame and change the programming, but if the work involves connecting new jumpers at a dozen distribution points and installing pair-gain units, it's actually much cheaper than the fee would be otherwise.
