To frustrated: what is your visa / work permit situation? If you are restricted to working for your current employer, then I think you are being exploited by your employer to some extent. They are paying you a below-market wage thereby undercutting their UK-based employers.
The starting graduate salary at Accenture is somewhere in the region of £32k (plus signing bonus). This is for people with zero experience.
On the other hand, if you are free from work permit restrictions, then its a market economy: you are free to apply for UK-based jobs at the big (or small) consultantancies. Then the question becomes whether your skillset and experience will get you hired.
Unfortunately I suspect you would be subjected to some prejudice here (some founded, some unfounded). Its not all about skills and qualifications on paper (Prince, Six Sigma, CFA, whatever), but about whether you can lead team of client and consultants, shape work and relationships with senior clients, and a whole bunch of other 'soft skills' stuff.
Since this is difficult to convey on a CV, recruiters will try to infer it based on your previous experiences. However, if your consulting experience is largely from India, the recruiter won't know anything about the type of work you have done, the working environment, level of client contact, or types of firms you have worked for. Therefore they will struggle to understand how good your soft skills are, and may reject you simply due to that.
This isn't the case for all recruiters, but I suspect the case for most. For example, imagine a recruiter has 20 CVs to read through in an hour. They will spend a few minutes scanning through - if they can't assimilate any of the information to their understanding of the consulting world, they will move on to the next one.
Finally, you don't mention what type of consulting you do. Remember that strategy consulting pay is in a different league to what I call management consulting, which is again on a different scale to IT consulting and offshoring consulting.