They took Tornado up to 100mph a few years back so it's do-able with the new build engines, although she has the restriction of no streamlining. Bittern was given special permission to do...I think it was around 90mph back during the 75th anniversary of Mallards run.
The problem with using preserved locomotives rather than new builds is the risk of breaking them by working them that hard, so the P2 would be the ideal candidate. Plus, you've got the 100th anniversary in about 13 years from now, so the other P2 project with the A4 like front might be done by then.
No one knows when HS2 will eventually be done, the original estimate was 2033...so, push that back by five years and you've got a good opportunity to do what you suggested as a celebration of the 100th anniversary of the run.
Plus you've got the extra historical fun fact that the London to Birmingham line was one of the first of the major intercity lines (after the Liverpool to Manchester) to open, in 1833. So there's the 200th anniversary of that coming up.
Yeah Tornado or P2 was what I was thinking of.