As Balmerhon said, offering the pet deposit is helpful and a lot of agencies have that built in now for landlords who are "open" to the idea of a dog, but not upfront about it.
The problem arises when they think of "large dogs" (even though anyone who knows anything about dogs at all knows that smaller dogs have a propensity to be noisier (and it's noise/cleanliness the landlords are concerned about)
When I desperately needed to move, I designed a flyer with my dogs photo (with a ruler at the side to show her height), a brief description about her and her age and more about how important to us she was and how seriously we took her care and her wellbeing. At the time, she was 11 and her emotional welfare and comfort was of utmost importance in our lives and we made this very clear. She was also a "barkless" breed (still relatively rare in this country) and known for a short, odourless coat and we offered a non-returnable security deposit of £200 plus a clause to say that any damage/odour or pest control problems would be undertaken by us if necessary. So we managed to turn a completely anti-dog landlord around and got our 2 bed victorian garden flat (newly renovated, brand new kitchen, carpets etc) He also knew how often she would be walked (3 times per day) and how long she would ever be left alone in the apartment (never more than 4 hrs at the very maximum).
I also offered to have the landlord round to the flat we were in at the time (all cream thick carpets!) to see for himself (he declined) - long story short- he never heard my dog, nor did my upstairs neighbours and I lost my dog in the time we lived there and I moved out immediately after she was put to rest there and I received all of our deposit back and a note from our landlords thanking us for being wonderful tenants and for leaving the flat as immaculate as we left there.
It can be done.....just ask the agents to only consider landlords who might be open to pets and a reference from your previous landlord if you have one might help.
Good Luck - I totally understand how worrying this can be.
This site used to come up with a lot of private landlord hits for me
http://www.rentamatic.co.uk/