'To this day' is a fixed expression in British English. It's much more common than 'till this day'.

I know you state "British English" but in American English, these two are interchangeable. :) We prefer 'to' though.

Yeah, I would say they mean pretty much the sme thing. The one thing I would add, I tend to associate to this day as for long terms things ie. for years and years while until is for shorter things. To this day sounds quite historical, I would say until now for things that are shorter term

Just my opinion but I believe it was always "to this day" , but some people confused it as 'til this day and that started to be used also. The word until is a pretext to something happening post "this day". For example, 'Til this day, not many people have shopped here. To this day, not many people have shopped here. They mean different things. The first one is proclaiming that starting today, people have started to shop here. The second simply states not many people shop here ever.