The agency in London responsible, Thames Water, will replace any lead pipe in the public network leading to your building if you agree to replace any lead pipe on your property within 3 months.
But I live in a "leasehold" flat (common in London). So "you" for the purposes of that agreement would be not me but the "freeholder", who is responsible for building maintenance. To get them to do anything, I have to go to a lot of effort to get action out of the "management company" hired by the freeholder (and probably then be blamed by other leaseholders -- most of whom don't live here -- for costing them money to replace the pipe). I followed up with them maybe four times before giving up. I'm not the customer of the freeholder or of the management company. Reading up on the impact on adults (thought to be low compared to the impact on kids), I decided to just run my tap for a few minutes every day and store water to drink for that day (wasting lots of water in the process). I notified the other residents, some of whom have children, suggesting I could help take it further if others helped out. Nobody responded.