I've had a peek back at your threads Icecreamlady and it was constructive dismissal that you were considering claiming wasn't it? What's the current situation with regards to your claim? As you will have seen from what I posted for you previously, constructive dismissal is very difficult to prove, particularly as you resigned without trying to resolve the situation internally first, and very stressful and time-consuming.
Are you really considering bringing a claim? You do realise that compensation will only be based on actual financial loss. If you get another job, your financial loss won't be very much, so it would be unlikely to be worth it, unless you are doing it to prove a point. Doing it to prove a point can be a valid reason, and is for some people as long as you are fully aware of the impact it will have on you. The decision should be based on what you realistically what to achieve.
Now I've said my piece on that, in terms of a reference, there is nothing specific legally that says an employer must provide a reference, although there are some legal points you could make if they refuse, depending on what type of work it is, to do with custom and practice and effectively preventing you from gaining employment.
I would suggest you ring your manager if possible and ask why she is refusing to provide a reference. She is certainly able to, but she is refusing. If she didn't feel able to gush about how wonderful you are given the circumstances of your departure, fine, but she can provide a factual reference about your dates of employment, attendance record if requested and what job you were doing.
Have you explained the situation to the agency? What's their take on it? How about contacting HR at your old employer and asking them to provide a reference. If you tell them your manager is refusing to provide a reference they ought to sort you one out fairly pronto given the circumstances.