Thames Water (and other Water Co's) are responsible for their water main, the stop tap and or meter fitted to their main and the pipe from that point to the property boundary.
The property owner is responsible for the pipe from the boundary to the internal property stop tap (and all pipework within the property).
If the pipe to the property needs replacing, it's for the property owner to arrange and pay for the work from inside the property out and up to the boundary.
The property owner will then have to pay Thames Water or other Water Co. to connect the new pipe to their pipe in the street / pavement. This needs arranging before any work is started.
Water Companies have in the past waived the charge for connection of a replacement pipe to their existing stop tap / meter where lead pipe was previously used, whether they do at any particular time varies on their policy at the time.
I don't beleive they ever have waved charges for replacement from their main across the property boundary and inside the property.