Let's break down your reasons.
1. Better pay for the same work: Almost certainly some consultancies will pay at or above market rate for relevant experience. However unless you're very good at hiding your true salary most firms will match your current pay given your situation (jumping ship less than 1 year into a job).
2. Work with more people = Maybe. Arguably the larger the firm the more pigeonholed you will be in a specific role with a smaller remit.
3. Have more client exposure = If you mean more late nights with the client pretending to laugh at their drunken jokes or getting the red eye into London City, sure why not.
4. Range of projects could be wider = Depends on your group and what you are aiming for.
5. Working in a capital city = if you get a 20% payrise in a new job but your living costs are 40% more, why bother?
My point being, don't be so quick to dismiss the advantages of your present situation and always know the true cost (and consequences) of any decision. But then, you're in Strat - you're supposed to know this already.