According to a study reported here, most of London is sinking and at the same time sea levels are rising due to global warming. So in the worst effected areas the net result is water levels rising by up to 2.5 mm / year which over the next 40 years would work out as a noticeable 10 cm. Not all is so bad - towards Northolt the ground is slightly rising due to the underlying geology.
Fortunately where I am is steady or slightly decreasing (light blue in the figure above). Phew! No need yet for life jackets or rafts!
What is more the same study identified that due to tidal effects London moves vertically 10 mm twice a day due to the weight of water coming in and out. That must be near the estuary rather than upriver here where surely there can't be enough water to make that amount of height variation.
Even so its hard to think of a whole city rising and falling - makes me think of this series of books I've just finished (recommend if you like that sort of thing).