I've been applying to a few institutes across UK and Singapore over the last few months. In the UK, I applied to Oxford, Cambridge and Imperial. Though I have limited full time work experience (3y+ this fall), I believe I have a very competitive profile. I work in India at a tech MNC, have some entrepreneurial experience and accolades in tech innovation/research .
Though I found success in Singapore, my applications in the UK were less successful. I only received an interview invite from Imperial, and it did not convert to an admit.
Now I do intend to apply to a few more institutes (Manchester, Cass and Warwick currently in mind), but I was hoping to get this forum's suggestions on any other schools I should target.
My post-MBA goal is to work in product management, hopefully in the UK. Any suggestions would be greatly appreciated!

93% of product managers in the UK don't have an MBA. 

If you want a top UK MBA you need to be a stronger candidate and have MBA career goals. There are several really strong MSc degrees in product innovation, development and management, at Birmingham, Cranfield, Strathclyde, UCL etc. 

You need a stronger use case for an MBA. An extra year would also help you to show capability, self awareness, values etc. 

Not to be too harsh but I'm not surprised that your applications were not successfully. And without an incredible GMAT score, I would be skeptical if you landed any of the schools you have in mind (at least for their MBA programs.)

I agree with Duncan, take an extra year if you are really targeting an MBA of this level. Otherwise, try a specialized MSc degree. The salary outcomes will be worse but more appropriate to your career level and goals. 

93% of product managers in the UK don't have an MBA. 

[Edited by srish96 on Feb 13, 2021]

Did you search LinkedIn to see where graduates of that degree end up> I imagine that for each one involved in product management 50 are in business analysis or systems analysis. 

Did you search LinkedIn to see where graduates of that degree end up> I imagine that for each one involved in product management 50 are in business analysis or systems analysis. 

If you want to work in product management, I suggest you study the profiles and career paths of those working in the field, with particular attention to those with your background. You might need a series of career steps, not just an MSc. 

If you want to work in product management, I suggest you study the profiles and career paths of those working in the field, with particular attention to those with your background. You might need a series of career steps, not just an MSc. 

I could see very mixed result on my research at LinkedIn. It looks like some folks haven’t got proper business analysis job. I am not sure whether it’s due to covid or any other issue.

I could see very mixed result on my research at LinkedIn. It looks like some folks haven’t got proper business analysis job. I am not sure whether it’s due to covid or any other issue.

It might be that they don't frame their jobs within the category of 'business analysis.' It's more likely that career paths out of this MSc would be labeled 'consulting,' 'strategy,' or potentially 'business analytics' or something analyst related.