The stunt coincided with severe flooding destroying houses across parts of Derbyshire and Yorkshire, which XR said was a stark reminder of the "very real risk".
The Intergovernmental Panel on Climate Change has warned of a rise of two metres by 2100, although climate scientists predict sea levels may rise between one and five metres.
Under new sea level rise projections, Stratford, Barking, Dagenham and parts of south and east London, East Anglia, Essex and Kent could be under water by 2050.
The head of the UK Climate Expert Committee Stephen Harrison believes the IPCC is underestimating the threat.
"We may be close to passing a tipping point for at least some of the large outlet glaciers draining the West Antarctic Ice Sheet, and this would commit us to significant sea level rise whatever we decide in terms of reducing Greenhouse Gas Emissions," Harrison said.
The Sinking House was built by Katey Burak and Rob Higgs.
In a statement, the pair said: "We want to respectfully raise awareness of the severity of the impending human-made disaster. We need urgent action to address the Climate Emergency and devastation of our beautiful and precious natural world, which is being decimated at an unprecedented and tragic rate."
The stunt received praise from some quarters. Frank managing partner Andrew Bloch labelled it "PR stunt of the day".
However, not all XR activities have gone down as well as the sinking house. Grayling head of consumer brands Frankie Oliver had some polite advice for the movement after some protestors tried to shut down a busy London Underground station.