It's a transaction tax. Setting aside that there's typically a 2% cost on buying and selling a house in the UK anyway due to estate agents and legal costs, and the average house attracts another 1.5% in stamp duty it's not a major obstacle for the majority of transactions, but it's still friction.

It would be far better to replace with a %age tax whether you move or not, but wealthy people in the south east don't like the idea of taxes on unearned wealth.