First thing that comes to mind grad is that you did a masters from kings. If your masters was in management or a mini mba type program, then some B-skewls might instantly turn you down as they will not take people who have done an MBA before.
Now regarding the grades - your perfectly fine. Due to the complexities and bias of cross atlantic grade comparison, a 2.1 shall do perfectly fine. It wont lose you any points nor will it gain you any. So your safe here.
Regarding PA, I'm not sure about the BOP practise, but there are a few people in their US offices from top B-schools. So if they are in touch with their alma mater, the name should be known. Whats most imp is for you to get into the firm, work hard and try to get promoted real fast. This is something that B-Skewls look at highly.
In terms of the top rankings - harvard wharton stanford MIT kellog are generally considered the best. Surely LBS and INSEAD are good but honestly there brand names doesnt carry itself in Latam and North Am.
You should be realistic abt your chances, I think that you can get into a good b-skewl. But not a top one. U'll need to do a number of things to prove your worth to the top mentioned ones. Your a good fit for a Faqu, Stern, LBS.
However even to get into those you will need to score highly on the GMAT, write some really compelling essays arguing your worth. If I were you I would concentrate on the US. This is becos not THAT many people from the UK go there for B-skewl. More importantly coming from a smaller outfit like PA shall do you well compared to a place like Acc or Deloitte from which many people apply.
Lastly planning is good but don't be navie. B-skewl is not the do all and end all of consulting or the corporate world. If your doing well in the firm, there may be no point of going to b-skewl. Secondly give yourself a year and see whether you like consulting and if its meant for you.If you don't like it then consider other options - Accountancy, IB, Trading, Industy.
P.S If you have a liberal arts degree, it would most definately increase your chances. I did ! :)