I need to appeal against a decision made by my UK university. I need a
list of about 5 top, UK-based lawyers who have most experience or
highly reputed in dealing with university students rights.

You will need to specify whether you require English/Welsh or
Scottish, as the two countries have separate jurisdictions and legal
systems.

http://www.lawscot.org.uk/ for Scottish
Click on Accredited Specialisms. There is no listing for Education,
but if this is going to go to a higher court you might want a Civil
Solicitor Advocate

http://www.solicitors-online.com/ for English/Welsh
There is a pull-down Specialisation which includes Education. 

You could also contact the National Union of Students Legal Services.
http://www.dur.ac.uk/c.j.neville-smith/NUS/Legal/NUSservices.html
http://www.nusonline.co.uk/

Owain

Please be aware that good lawyers are VERY expensive and, if you start
litigation, there's no going back.

This is going to cost you a LOT of money ...

And is it going to be worth it?

I doubt it.