Are fixed-term research funded staff such as post-docs entitled to redundancy rights, such as severence pay at end of contract?
Yes. If you refer to your contract, you will find it is a contract of employment (and probably explicitly states that you are an employee of the university*). Indeed, some universities issue permanent contracts, with a "we'll make you redundant once the funding runs out" clause, to their postdocs.

A few other points:


If you wanted to claim redundancy benefits, you would have to wait for the university to actually let you go. This prevents you leaving before the end of your contract, so will limit your ability to look for a new job in a timely fashion. The university could just shift you into another role to avoid the redundancy costs (especially if it's one you'll want to leave); although, hopefully, most wouldn't be that cynical.


(There's a possibility that they could also require you to apply for suitable, open internal positions, but I don't know whether they could seriously claim your failure to do this equated to leaving voluntarily.)

From your own link, there is no notice period on the non-renewal of a fixed term contract; so a notice period on non-renewal of the contract would only apply to people who, by virtue of over four years of service, have become permanent employees:


  Fixed-term contracts will normally end automatically when they reach the agreed end date. The employer doesn’t have to give any notice.

Postdocs are not students or trainees. Here's the definition of those two categories, from the Fixed-term Employees (Prevention of Less Favourable Treatment) Regulations 2002 (part 5, exclusions) (emphasis added):


  18.—(1) These Regulations shall not have effect in relation to a fixed-term employee who is employed on a scheme, designed to provide him with training or work experience for the purpose of assisting him to seek or obtain work...
  
  [cut, funding info]
  
  (2) These Regulations shall not have effect in relation to a fixed-term employee whose employment consists in attending a period of work experience not exceeding one year that he is required to attend as part of a higher education course....
  
  [cut, references to the acts that define a HE course]

The pay grade is irrelevant. 


*Weirdly, I have seen employment contracts that state you're not (and not for self-employed contracting arrangements). I don't know why because a court wouldn't find someone not to be an employee just because the contract says so.