As of yet, there is no way to firmly establish the number of transgender people living in the U.K. One percent is a rough estimate.
In 2018, the Government Equalities Office published a document that gave a tentative estimate of 200,000-500,000 trans people living in the U.K; however, the LGBTQ rights charity Stonewall puts its own current estimate at 600,000. Assuming this last figure is accurate, the trans percentage of the U.K. population (just over 67 million currently) would be roughly 0.9 percent. However, the actual number is likely to be higher, owing to methodological issues with obtaining information about transgender people.
There are multiple definitions of the term transgender, and using any one definition risks accidentally excluding people. Even using the broadest possible sense of the term (which includes any individual whose gender identity does not align with the sex assigned to them at birth) risks alienating trans people who have undergone gender reassignment, potentially including surgery, who wish to no longer regard themselves as "trans" but as simply men or women. Another issue is the relatively small sample universe. The small proportion of trans people in the overall population makes it challenging to gather an adequate number of responses in surveys and studies, making it difficult to establish the accuracy of survey data.
More reliable data is likely to be available when the results of the 2021 national census are released.