We just moved about a month ago and we were even turned down offering to pay 6 months up front! Those were smaller agencies that turned us away, just weren't used to dealing with international folks (despite our area being full of corporate expats). We found that once we raised our price point and looked at more expensive homes that many locals would struggle to afford, it became much easier and the agents and owners were happy to take our money. We didn't try any private landlords, of which there were few.
We also have a large dog and found that pets can be negotiable, but we did have to pay a significant pet deposit and agree to pay for a professional deep clean upon vacating the property.
In short, money talks and if I wasn't in the position to cough up the dough, it would have been very difficult for us (we're in Hampshire). YMMV!
One other thing, we didn't have a local bank account and that was a problem as well with the smaller agencies but the larger agencies were fine with us doing an international transfer for the initial deposit. Banks here like a local address before they'll open an account for you so it can be a bit of a catch 22 at the beginning! Once you get the rental contract the bank account's a breeze and life get's much easier!
Best of luck to you!