Routes to transition into IBD/VC after grad scheme in IM? Masters?

Hi guys, I have a question about taking a masters in order to transition into IBD.

Here's the situation:
I've just recently graduated with a 1st in Bio MEng at a semi-target UK uni (think- Nottingham, Bristol, Manchester) and have a FT offer for a 1 year grad scheme in Investment Management which starts after summer. The scheme is rotational so it covers FO/MO stuff. However, my true ambition lies within M&A or VC/PE fund, focusing on the healthcare sector. My past experience includes a SA in MO and a 1 year placement at a FMCG company.

So here's what I've been thinking. I could finish the 1 year grad scheme and apply for Masters in Finance (LSE) or Masters in Management (LBS). Then I will try my luck again for a pre and post masters SA and/or FT, respectively. I'm not too fussed about the uni at this point of time. But my real concern is whether the masters would add value and increase my competitiveness in FT IBD recruitment even without prior FO IBD experience?

Cheers!