There is evidence of sudden level changes in the form of certain estuaries. Sea level fell quite fast, geologically speaking, creating a new steep run for the river down into the sea. The resulting fast-moving water caused rapid erosion of a steep-sided valley. Then sea-level rose again, and the valley flooded with seawater, preserving its steep underwater form because erosion below the low-tide level is very slow. Take a look at Dartmouth or the Wye. It's very unlikely that the level of the UK land-mass could change fast enough to account for this.. The UK is geologically pretty stable (large earthquakes are rare, for example). The Andes are an example of rapidly-changing land levels - frequent catastrophic earthquakes, river-flows reversed in their valleys, and beaches raised tens of metres in mere thousands of years, as noted by Darwin. BTW glaciation creates a straight-ish U-shaped valley (or fjord), river erosion creates a wiggly V-shaped valley, so we can tell these southern estuaries aren't the result of glacier erosion.
One can also calculate what sea-level will be if all the ice-caps melt. At the very least, that should put you off investing in any land or property anywhere near to present sea-level! More seriously, the worst-case scenario is so bad that I do think we ought to heed the precautionary principle before it's too late.
Worst-case is permafrost thawing releasing methane causing global warming causing more permafrost thawing ... a positive feedback loop that won't stop until all the permafrost has thawed. There is geological evidence that such runaway warming events have happened several times in recent geological history. There is also geological evidence that the long-term stable (say 30Myear-average) situation for the Earth is with no large ice-caps at all and a MUCH warmer climate regulated by percentage cloud cover. Ice causes instability and positive feedback loops. We live in climatologically interesting times.