Realistic chances for UK MSc Program

I am entering my final year at a non-target university in the UK. I am aiming to apply to target universities for my MSc to improve my chances of securing an off-cycle or graduate role in IB, PE, or PC. I am currently achieving a low first-class degree and have completed two summer internships, one in asset management and another as a portfolio management intern at a wealth management firm.

Considering my profile, I would like to know which programmes are realistically within reach and whether taking the GRE or GMAT would significantly enhance my profile.