Hi! I am British and I know it's annoying when people point this out, but there is a huge variety in British accents. You're probably referring to the Standard English accent - this sounds completely different to Scottish English for example. I have a northern English accent and I honestly am not a fan of Standard English because it sounds so posh and dull to me, but that's more because of cultural and social reasons that non-British people probably don't care about. My favourite British accents are Northern Irish and Newcastle because they sound very friendly and melodic. I also like Liverpool accents, but these are very hard to understand for both foreigners and native English speakers.
Edit - just seen your comment saying you live in Ireland so I guess you know all this!
To be honest, I think American accents are better for non-English speakers wanting to learn English. They are easier to understand, mainly because you probably hear them a lot more - in movies, on TV, in music (even British pop singers usually sing with an American accent).
It's completely your decision which accent you want to try to stick to when you're learning English, whichever sounds best to you. My personal opinion is that foreigners learning English seem to pick up American accents and sound fluent in them much more so than when they try to do a British (Standard English) accent. This might just be my view because I am British, but I do think it can sound a bit clunky and forced - an American-ish foreign accent speaking English sounds more natural to me.
(Btw - Australian and Standard English are pretty similar, obviously they do have a lot of differences, but I know a lot of Americans can't tell the difference lol. For me, if someone is speaking in an Australian accent, unless it's a really strong one, it can take a few sentences before I realise it's Australian and not Standard English)