Archaeology is mostly tax payer funded, although it is getting more common for sponsorship from companies. Quarrying and oil companies use environmental data as it helps them decide whether to set up shop there. Also it is compulsory to have an archaeological survey for something the size of HS2 when being built, especially when it is in London. London itself is one massive museum and underground are some many fantastic and important discoveries to be made.
My suggestion is this. Why not explore London's history to the maximum. It is a great city, as Boris always says, and you can never know too much about its past. So let's find out more. We should force for an extremely detailed survey to be done of the HS2 route. Let's get to know the area really well along the HS2 route and force a very long survey that would hold it up for ages. Or better still make HS2 take a route of historical areas so we get to know even more, and waste the time of the builders. Maybe government will stop it then, or by the time it finishes a more sensible government will scrap it. Archaeological investigations across the HS2 route will also save money because, whatever the bill for the digs will be, it is certainly cheaper than building an irrelevant railway.
Let's get Tony Robinson and Time Team on the scene to stop HS2.