Depending on your current mental and emotional state resulting from the split, I think it could be a risky move to come on your own at this point imo. If you're fragile and this is a painful split from a serious long term relationship, then there is the danger that you won't get to experience Australia properly whilst here due to being preoccupied by trying to come to terms with the split. You will inevitably feel lonely and your mental state could really cloud your judgement. Personally, if I was in this scenario I would delay my entry to Aus and get my head straight whilst in UK amongst friends and family.
However, if it's less of a big deal than that and you're simply feeling a bit gloomy, then coming out here will be the best thing. You'll be over the split within seconds!
Just reading between the lines of what you've posted. I definitely would not fly out without ensuring everything is as sorted as it can be with your ex. The last thing you want is it to be affecting you when you come out.
Good luck