I've read the horror stories here myself, but have transited, as well as departed LHR several times just in the past couple years at this point, and it's honestly been quite easy. I try to ensure I have everything precisely right, of course, but I've never had any trouble. I have, however, had tons of annoying issues at tiny one-airlines regional airports in the States. It really depends on so many factors, so long as you are prepared with the right sizes, etc.