Hmm. Perhaps it is the case that it is recently becoming more common in BrEnglish (outside of dialects and 'ill-gotten'), but I'm afraid my first instinct is to be sceptical about this without seeing some actual data for it. People's impressions of what is new in a language or is in the early stage of increase are often unreliable because it's a well-known selective attention effect - just because you have only just started noticing something, you think it's new, when in fact it's been widespread for some time. Then because you are paying more attention to it, you notice it more frequently, and conclude that it really is on the increase - when in fact any one person's experience is too small and biased a sample of language to draw sound conclusions about wide-scale change.
I just had a look at the full OED entries for 'gotten' and 'get' and it says that Webster 1864 gave 'gotten' as "obsolescent". But again, that's a subjective impression. I would want to see corpus data to see when/if it started picking up frequency in BrEnglish.
Also worth considering that 'gotten' in AmEnglish is used in a different range of contexts to 'have got': it's used for senses including causation, acquisition, becoming, movement - it's only for non-possessive senses. So it actually expands the range of senses in which 'get' can be used.
Also, languages innovate, and we all need to get over it.