It largely depends on the area, but people can be abused about anything that bullies, especially drunks, perceive as "different" in ANY way. I have been verbally abused because I look "gay". I am a white person living in a mostly white country, but I have been racially abused by young adults while walking through some parts of town. I originally planned to come to England and live permanently as a woman, but that has not happened yet for a number of reasons, fear not the least of them. There have been news stories recently that claim that Britain is unsafe for trans people, e.g. the one about a British trans woman being given asylum in New Zealand.
Having said that, many trans people do not report any major problems. I would expect you to be reasonably safe if you are on a fairly short visit and avoid obviously run down areas.