Non-Big 4 ACA to IB/ER/PE?

I’m currently studying for my ACA and will be qualified next summer. I find accounting really boring and would ideally like to be able to get into IB/ER/PE, anything where you’re using financial modelling and valuations etc, I find all that stuff really interesting. 
 

I’m aware of how competitive these jobs are and have no Big 4 or financial modelling etc prior experience. I’ll also be 29 by the time I qualify. 
 

Is it still possible for me to follow this career path (I’ll be based in London)? My plan would be to get into transaction advisory services / corporate finance once qualified (ideally Big 4) and then try to move across after a few years. For self-study I’m currently taking a few free online courses to learn about financial modelling and valuation methods. Unfortunately an MBA isn’t an option as it is too expensive. 
 

Any advice would be very much appreciated, as if this isn’t really feasible I’ll just have to accept my fate in accounting. 
 

Thank you!