According to the Newcomen Society.
There are no true Newcomen engines in existence today, but at the Black Country Living Museum at Dudley there is a unique full-sized working replica of the 1712 Dudley Castle engine, based on a drawing of 1719. The engine is operated under steam from time to time, and can be observed by the public.
At Dartmouth there is a small atmospheric engine donated by the British Transport Commission, and erected by Mr Arthur Pyne, member of the Newcomen Society, in 1963. Its early history is not certain, but it was used by the Coventry Canal Company from 1821-1913 for pumping water into the canal at Hawkesbury Junction. It is fitted with a later form of condenser, but has the traditional timber rocking beam. The refurbished engine house now has a hydraulic mechanism and some descriptive material on display.
There is another, much modified, atmospheric engine at Elsecar, but this has cast-iron beams of a later period, parallel motion and a separate condenser patented by James Watt in 1769.
http://www.newcomen.com/thomas.htm
The past is a foreign country: they do things differently there.