I just had the same thing happen as well! Moved into a new flat last weekend and it was FILTHY. We called the estate agent and they basically said: the previous tenants should have cleaned it, oh well, too bad. We managed to get the landlord's number and she was not that bothered either, until we pointed out some obvious health and safety violations in the flat and threatened to withhold rent until they were fixed.
What helped in our case was pointing out to everyone that with the new deposit scheme, they can withhold some money from the previous tenants' deposit and use that to reimburse us for cleaning, so they wouldn't be out of pocket themselves. (We had lots of photos of how filthy things were, so keeping some of the deposit would not be difficult.) The agency agreed to reimburse us at the rate they would pay cleaners, 14 pounds an hour, so at least we will get something back for the hassle.
I do sense a bit of a cultural difference here as well, not sure if I'm right? But I have moved around a lot in London, and the sense I get is that landlords don't expect to have to fix things up between tenants, unless the place is completely destroyed. Back home, even moving into really cheap apartments, everything would be clean and ready to go. Here, it's much more hit-or-miss. From talking to friends as well, it seems like landlords are willing to let a property slowly degenerate until finally it's nasty and they have to do something.
(I realise these are big generalisations, again just my perceptions from my experiences and talking to friends.)
Anyway my two cents: just because you're dealing with an agent, don't expect a higher degree of professionalism (if anything, they can just trade blame back and forth with the landlord). Obviously it's good to get something in writing but this can be hard dealing with an agent (we were told for example that they can't modify the lease template that all their offices use, which is probably BS but what can you do?) And take photos of everything and demand compensation for cleaning. Sometimes the 'pushy American' stereotype comes in handy...