The other thing is that the building in which the London Stone is displayed is also coming down (planning approval was actually granted as long ago as 2002). The Stone itself will go into the Museum of London for while, before being put back into a better display in the new building on the current site.
The Stone is a bit of a mystery. It's been suggested that it was either a milestone from which all distances in the Roman province of Britain were measured, or that it was part of a stone circle that stood on St. Paul's. Unfortunately, there's no documented reference to it before 1198, though John Stowe, writing in the sixteenth century, claimed that there was a tenth-century mention of it. It is generally accepted that there's a lot less of it than there once was (and I mean a lot - what's now no bigger than a large television was described as 'very tall' in 1598). And that's about it. My gut instinct tends to be 'not Roman', but I don't have a good reason for believing that, and I'm not too happy about a pre-Roman existence either, which tends to get mixed up with mediaeval legends of the pre-Roman foundation of London - legends I don't believe, as I think they're more about promoting the new Anglo-Norman capital of London at the expense of the old Anglo-Saxon capital of Winchester.
Anyway, I'm pleased that both monuments will get a better display than they currently have, and perhaps Londoners will become more aware of their heritage. Both objects feature in my regular walk for the students around Roman London (as well as the very neglected Roman beam in the forecourt of Church of St Magnus the Martyr on Lower Thames Street), though I'm guessing that this may be the last year that I'll be able to visit them both.
And what nobody's mentioned is that these two redevelopments offer opportunities for some very exciting archaeology. I bet MoLAS (Museum of London Archaeology Service) are champing at the bit for a chance to get back to the Mithraeum site.