The issue is, and always has been, that in the UK property is as much (if not more) a financial investment as it can be a home. This is a cultural thing, for centuries people's fortunes have been tied to land ownership, from the sublime (Duke of Westminster end of the scale) to the ridiculous (eg tithed cottage). This has become, over many, many years, so much the case that class, upward mobility, access to education and good health can all be turned on their heads by this one thing alone.
Nobody would care if this were a tax on artworks, or cars, or other valuables items at £2m +. These are all privileges available to the rich, with no direct correlation to others not being able to afford their rent.
In other cultures, people put their money into family businesses, into buying farmland, into government bonds and stocks/shares, into education funds. Not so in the UK. If people come into money, more often than not property is at the top of the list.
I don't know what the solution is, but I do know that a blanket tax such as the proposed mansion tax is not the answer. The problem is complex and nuanced. This tax is like using a sledgehammer to crack a nut, missing, breaking your toe and allowing hundreds more nuts to accumulate in the meantime.