https://en.wikipedia.org/wiki/London_Mithraeum
I'm told that lots of the office buildings in the area have Roman ruins just kinda bricked in and sealed in the basements. i.e., they get discovered during excavation, measurements are taken and whatnot, and while it's worth saving them it's not worth putting them on display and making a big deal out of it.
Or in other words: "We know this site is teeming with archaeology. You don't get to trash it unless you pay for a proper dig before you start"
In order to get planning permission, developers need to do a historical/archaeological evaluation [0]. Occasionally I've seen notices to contractors at sites that warn work is to be halted if bones/pottery are found. I'm sure the nearby universities get involved with this as well.
[0]: https://www.cityoflondon.gov.uk/services/environment-and-pla...
Also, at dig sites where there's likely to be historic remains in the UK, there's work done to ensure the conservation of the archeology likely to be uncovered.
It's called archeological excavation, if you want to do some Googling. Also, have a look at the Museum of London Archaeology. They do a lot of stuff with this.
Source: I work just down the road from three current construction projects going on at major archeological sites and asked them the same question.
[1] http://new.archaeologyuk.org/news/cba-response-to-new-neighb...