Should I be targeting top or mid-tier schools for an MSc in Finance with my profile? Does my profile give me a solid chance of landing a place at a well-ranked university?

Apologies, this will be a slightly long post as I want to give all relevant details. Any advice would be really helpful!

I am a current student at the University of Glasgow (18.9/22.0 GPA, so on track for a First class honours degree) in Mechanical Engineering with Aeronautics. I am interested in breaking into finance or consulting, and as I have no finance/consulting internships under my belt, I am looking at completing a Master's degree as my best way of doing this.

• I will graduate in 2026, so would be looking to start my Master's in Summer/Autumn 2026
• From practice GMAT, I'm looking at a score in the region of 700 (official practice exam scores of 735, 695, and 695 so far)
•  I will have completed 1 full year in industry with an engineering internship, but as I said, nothing in finance/consulting - how much does this weaken my applications?
• Throughout university, I have a variety of roles in clubs and societies, including some leadership roles. These are mostly (but not exclusively) engineering clubs
• While I will be able to get letters of reference from professors/colleagues, I fear that my university professors will not know me well enough to write a particularly outstanding recommendation letter, so this would definitely be a weaker area of my application

With these factors in mind, would my strong GPA and GMAT scores, alongside strong quantitative Bachelor's, make it sensible for me to apply to top business schools? E.g. LSE, ESSEC, Edhec? Or would the negatives mean that my chances are minimal? Would I be better off targeting more applications at schools such as Nova, Bocconi, EM Lyon, Warwick, that are slightly lower in rankings but sitll provide good outcomes? I would be grateful for any advice!