Consulting is an attainable goal for you, I have seen the move from Global Mobility to Consulting made before (very rarely). However, you'll probably find it difficult to do within your current firm (which I presume to be EY or Deloitte.) The skills are just too different and there will be limited pull.
You probably need to focus on less conventional consulting firms. Second tier niche players who like the sound of ex big 4 but aren't full of ex big 4 consultants. Consider firms that have consulting arms as part of other businesses (e.g. the outsourcers -Capita, Serco etc). Also look at project management consultancies like Moorhouse (whilst these are full of ex big 4 consultants, they'll appreciate your skills more). Given your background I'd say the type of firm is more important than its sector at this stage.
The most critical thing you need to do is to get your CV in order. You need to turn it from a tax CV to a consulting CV.
It's likely you've got some great transferable skills and done some great tax work - but this probably won't be immediately attractive to a consulting recruiter.
Instead, focus on the work you've done that has been project and change-based - likely to be outside your core day job. E.g. practice contributions, managing/improving complex administration tasks. If you've not got any experience in this then get some - but you've probably got more than you think. Then get feedback from someone in consulting.
If you're not sure which direction you want to take your career then consulting is probably a good option. It will give you more options than your current role. It goes without saying you should get a detailed understanding of what's involved though. Despite its significant downsides, it's still one of the better parts of the big 4 to be in.
Best of luck