Don't worry, you are wrong as far as ownership is concerned, so the law is on the OP's side.
The first external stopcock and pipe leading to it are the property of the water company, if they are on private land. If the stopcock were on public land, the water board owns the stopcock and the pipe as far as the boundary.
If TW were to install an additional stopcock at the boundary, or in the public land outside, it would still own the pipework up to and including the existing stopcock. Since the OP does not own the existing stopcock, it is not his to maintain, and the ownership of the pipe would not suddenly change just because the water board has fitted an additional stopcock. In any case, cutting into an old pipe rather than replace an existing valve is hardly a shortcut, so I can't see TW even bothering to try this workaround.
What I'm not sure about is whether the water board is required to re-lay the block paving to the current standard, and I suspect the answer is no. If you're lucky, though, TW's plumber may be able to repair the existing without having to dig it out, as Moonlight has stated.