It will certainly help once you have your ACA or ACCA designation under your belt, but for a Top 5 school you'll probably need more to stand a realistic chance. Given how many accountants apply for MBA's immediately post-qualification, the most successful are those who have picked up their designation in more "prestigious" firms and practices (in addition to strong academics and extra-curriculars).
Your best short-term option is to stay put and work like the devil to excel and stand out. The detailed set of options seems to be:
1) Stick with GT Audit, work your ass off, qualify, stand out as a star performer and get your name known, get accelerated promotion as a means of demonstrating your abilities, then apply to b-school with 5-7 years PQE
2) Switch to a higher profile accounting and finance career track e.g. Big-4 Valuation and Strategy, I-Banking, respected finance programmes in industry (GE etc.) Given the academics situation, this may be something you do post-qualification and having demonstrated your ability within GT.
3) Do something spectacular outside of work, drop out of accounting and start your own business. To be honest, this is probably the least realistic option. Desire to get into b-school is about the worst reason for becoming an entrpreneur, but if self-employment is something you're drawn to anyway and can make a success of then it's worth bearing in mind it can help prepare you for an MBA.