Accurate estimates of the sizes of transgender populations are hard to come by, but according to an article in The Times on Thursday, there are about 650,000 people in the UK (around 1%) who identify as transgender. The article does not cite a source and, unfortunately, the online version is behind a paywall (to which I have no access).
In an article from nine months ago, The Guardian cites a ‘conservative’ estimate of 0.2%, or around 130,000.
I was quite surprised to learn that this number was so high. For comparison, the 2011 census found that around 430,000 people identified as having Chinese ethnicity, and that around 270,000 identified their religion as Judaism. These groups, as well as many other minorities, are not represented well in Parliament or other high-ranking positions.