First of all, look for a place with wood or laminate flooring, at least on the ground floor. People without pets can be incredibly biased against cats + carpets, even if your cats, like mine, are housetrained and wouldn't dare pee on or tear up a carpet. I've found that this bias isn't applied to dogs nearly so much as cats, which makes little or no sense, and as a cat person makes me go
then
.
Secondly, once you've found a likely place, make an appointment to see the place and have a walkthrough and THEN bring up the cats. Don't tell the leasing agents at the beginning, as inevitably they'll automatically say no. All three places we've lived in the UK have been advertised as "no pets" - by waiting until after we've seen the property (and therefore decided whether or not we want to fight for it) to mention the cats, we've essentially charmed the leasing agents into contacting the landlords to get "special" permission for the cats. (Having a good reference from a previous landlord can only help in this case!) Also, offer to pay a pet deposit! We've offered in all three places, and have only had to pay once. In this economy, a lot of landlords would rather run the risk of needing to replace some carpets, etc. (especially when they can charge the cost against your bond or pet deposit) than have a rental property standing vacant for any period of time.
Obviously, I don't live in London, so I don't know how quickly properties go in the area in which you are looking, but up here there are far more vacancies than available tenants, so we have a bit more bargaining power. Good luck with your search!!
Yes! All of this! We've got 2 cats in central London. We have now rented 2 places that were okay with our cats. The first time, we offered an extra 2 weeks deposit (so 8 instead of 6 weeks) and a "pet reference" from our last US landlord and that was that. Our new place, that we're moving into soon, didn't require anything additional at all.

In both cases, we rented places with 100% hardwood flooring, for peace of mind as well as ease of cleanup (we've got a barfer).
In a lot of cases, the estate agents are just being lazy and don't want to have to do a bit of extra work calling the individual landlords to see if pets are okay. And I'm not sure if your cats are indoor-only (nevermind the cultural differences for now) but we really emphasized that (and it's 100% true) to make it clear that our cats wouldn't disturb anyone else in the building/area.
I've only run into one place that was adamantly NO PETS and it wasn't the landlord at all, it was the building, which had some medical offices on lower floors and didn't want any pets at all, lest it put off their higher-rent paying commercial tenants.
Also, for searching purposes, we condensed our two cats into one.

Somehow it seems less ominous to estate agents. We fully disclosed both in the end.
Good luck!