Just wanted to add that both are about right I am afraid, it is increasingly more difficult to rent with any pet, let alone two dogs.
You might have better luck if you can rent a whole house w/garden, or a garden flat (more expensive usually, but necessary for dogs I believe- even city dogs- there are always times when a dog injures a paw, has loose tum etc) or the lower half of a detached property for example. It's mostly agencies that won't allow pets, so finding ads for private landlords might be better (but if they agree to let you keep your dogs there, make sure you get it in writing)
Some agencies will allow approaching the landlord/managing agents & ask for a premium on your deposit ( for example, I had to pay £200 for anything that might involve fleas/blocked drains/inside soiling etc). (heavens forbid)
I was lucky and found someone who was willing to let us try- I provided a "bio" of my dog, explaining how important she was to me, how important her care was to me, I provided the cutest picture I could ( emotional blackmail always goes down well!) and I also offered to pay an extra £50 p/m for the first 3 mths to prove intent etc - it worked, the flat was immaculate, all cream and white and I got my whole deposit back and they didn't retain the flea money or cleaning fee. In my next apartment, I used the reference from the first landlord and the agent for the second one and I also invited the new landlord around to "meet" my dog- he trusted me also. When she died in February - I had to move out very quickly, I could not stand to be there any more- I had the loveliest letter from my landlord to say thank you for leaving the flat in such an immaculate condition, being wonderfully quiet tenants and if I ever needed anywhere else to live or a reference, they would happily provide me with one.
So, you can get lucky, but it takes time and effort and extra money.
I know you will want the dogs to come with you, but are there any other viable options for you to come and find somewhere suitable first? It would be better for you to leave the dogs behind if possible for a few months than to risk you all being homeless over here because no-one will take you with two dogs-or you are asked to leave because of say, your dogs barking (I am not saying they will or do, but they will be experiencing enormous change themselves and it is noise more than smell/soiling that landords care about).
Good Luck, I hope you find somewhere,
Sheril.