I am having 13 years of experience as business analyst and looking for MBA in UK as a route to get work visa into product management. I am confused about in which universities should I apply. I do not have GMAT score.

You should attend a very good business school if you want to work in the UK: that will mean taking the GMAT. Take a look at:
GMAT Tiers - strong schools for your GMAT www.find-mba.com/board/27082

Best MBAs for international students' placement http://www.find-mba.com/board/41143

Thankyou Duncan for the reply.
Though I am  too late for Sept 2023  but still applying in Cranfield, Lancaster, Manchester, Birmingham, Durham and Edinburgh to see if I can take their internally conducted exam or based on experience if the profile can be considered.

Also, want to check if can I apply in Jan 2024 again (with GMAT score) in the same universities If I do not get admit in  Sept 2023.

[Edited by Poornima Maheshwari on Feb 23, 2023]

You can sit for GMAT and target better schools next year if you prefer. However, for September/October ‘23 session, you can confidently apply to Lancaster, Durham and Edinburgh. Your application can be well considered without a GMAT score. Lancaster will also most likely assess your application a bit faster because they will have less applications this year having dropped off the FT rankings. 

Manchester has its own variant of the GMAT. It’s not quite easy as many people think but you could give that a shot. Warwick also has its own administered test in place of the GMAT, if you don’t have the GMAT. 

Make a run for Durham and Lancaster. 

[Edited by Obinna on Feb 23, 2023]

Thanks for the guidance. 
Will apply and keep you posted in case I receive the offer. Though I have an apprehension that being an international student I would be the employability aspect from these universities.

Thanks,
Poornima

More or less all the students in these MBAs are international students, so you should be not concerned. If you don't have UK work experience and are also changing role, I strongly recommend Manchester. It and LBS have a longer format that is idea for career changers.