Broadly speaking you're right, but in London in particular housing stock growth has been significant in the last 10 years but it has had consequently little effect on housing price deflation[0].
There are many theories as to why that is, but a personal pet one is that London is lacking in housing stock across the market and as such it is economically more viable to build at the middle and top end of the market where profits are higher than at the low end. When this is combined with a record low investment in local government social housing in London you get London's extreme housing market e.g. demand is high, but supply has all gravitated to the place where returns are highest