Finish your grad scheme first before you look at moving - it will only harm your chances to leap too early, but around the 2 year mark is about as good as it gets for exit points in your first role, and could be as little as 1 year. Your reasons for wanting to move into consulting are quite sound and will come across well, so use your time to brush up on your maths (GMAT level) and case studies - I think Tony R and the TopC guys have some guides etc for case studies and there are plenty of resources online to practice GMAT maths. As for telco consulting firms, a little research (also a useful skills to develop for consulting) on google should throw up a good long list of companies to approach, as should taking a look at the advertisers here on TopC.
I am assuming you achieved a 2:1 from a decent Uni, and have good A Level grades - As and Bs at least. If you don't then I would advise not to get too optimistic.