Obviously things happen, but there is very great variation in parts of the UK. Such a headline for the area in which I live is very heavily over the top. That said there are areas of some of the larger cities in which I would be very careful and probably avoid totally at night. They are the same areas which one would avoid when alone, whoever you were. As I said, things can happen, but at work in healthcare over several years looking very feminine with obvious makeup I never had any less than accepting collegues and only one vagely hostile look (from a patient later to be very friendly) on hundreds of home visits all over the East Midlands UK to all classes and races of people. On holidays I have had some minor abuse in other areas (for example - the West Midlands of UK - from what I have been told, and reported in the news, a generally far more abusive area for people in general), and as I have said elsewhere, in Scotland (Glasgow area) where for some reason women are far more abusive (very minor verbally only). From my experiences the South / Southwest seems to be the most accepting areas, in which no-one appeared to notice me at all (short holidays). Like most places though, inner city areas are generally the most hostile, with small towns in my experience not being particularly better in this respect. I have not visited such as London since changing, but with it's variation in areas I would suspect there are good and bad places. I have noticed that in some areas the authorities jump heavily on any abuse, but I suspect that is in areas in which the crime figures are lower than average anyway.
I have noticed some of the national newspapers cashing in their lot to oppose the general trend toward acceptance. I don't often read them, but my mother gets the Daily Mail which I read when I visit. I have noticed on several occasions what appears to me to be a deliberate attemp to provocate the masses to campaign against any change for the better. If a paper were to be called transphobic I would personally nominate them.
Obviously not living over there in the USA means I am not familiar with general life of trans people, but theoretically here, although there are minor differences in law by country, most are general so it is probable that local social conditions / norms have more effect on life than the law. This is probably at it's height in some 'estate' areas of some cities where the law of silence exists and to 'grass' literally could mean at minimum a good beating and permanent hostility (for most anyone).
You have made a significant step in improving your life by opening out your thoughts. Every small step you can make is an improvement. If you feel you cannot go out, begin to live how you feel at home. Take baby steps if you need but keep moving forward. You may amaze yourself by how quickly you move, particularly with mutual support from people here.