Don't worry at all about your undergraduate. Most uni's in the UK will look past it if you have performed well in your Masters. If you want to boost your chances before applying, I would say deepen your knowledge in your chosen research area. Do some really focused reading and volunteer with a relevant organisation. If you can show the selection panel passion, focused knowledge, and commitment to researching independently, you will do just fine. The Masters distinction can be used to support and compliment these. In fact, the improvement from undergrad to masters shows your determination and may work in your favour!
I did terribly at undegrad and was overwhelmingly unmotivated throughout - even retook one year. It was only after pursuing something I was more passionate about that I was able to, like you, get a distinction in my Masters. I've since started my PhD.
Good luck!