Neetu, from your post it sounds like you are just starting to research the industry.
If that is the case I would start by reading up as much as possible about the different roles that may be of interest to you, and then get some professional advice on your CV, cover letter, the application process, interviews etc. Good recruitment consultants will be able to help with this, or you may need to pay someone. Without this you really stand very little chance.
You are probably aware that there are countless doctors applying to consulting firms at the moment, but you may not be aware that the application process is much more vigorous than you will have been through in medicine, so only the few that are completely prepared will get in. In addition I know that a couple of the top firms in London have recently hired out of the NHS so they may not want/need any more doctors. All that being the case, if you are sure about leaving medicine I would also start to look at plans B and C if consulting is Plan A.
If you want to work in one of the more prestigious strategy companies, then realistically an MBA from a top school will be your best route. Forget other Masters or MPHs - these companies recruit MBAs from just a handful of schools.
Speak to as many people as you can but don't contact any firms until you are confident that you can hold your own in an interview-type discussion about healthcare and the consulting industry - treat every interaction as an interview.
One last thing - if, in an interview, you say that you want to work in consulting because the NHS is in a 'right state', you will not get a job. Think pulls rather than pushes.