And even if they specify no pets, still ask anyway, sometimes the offer of the deposit and a lot of money up front will sway them.
I have also seen people talk of providing doggy references from previous landlords too... love that!
Partial landlord here : I think, if the landlord lists with an agency, they automatically put "no" for pets. ALWAYS ask. Our tennents asked us and, as pet owners ourselves, we were okay with it but we did ask for extra money (and, as per our contract, we expect whenever they move out, that the house will be cleaned to the standard that it was prior to their moving in- which was brand new - so if there's any stains left from the cats, we will keep part of their deposit to remedy that etc.). It never hurts to ask. Worst case scenario you get a no but it's not the end of the world as there will be somebody else who's okay with it. If you come ready with previous landlord's statements saying how well behaved the dogs are as well as showing your flexible and willing to make sure it's little impact to their property (by agreeing an additional pet deposit, etc.), tha twill show that you might be somebody they are more willing to work with opposed to somebody who says "I have dogs and I expect that you should let them in because they are my babies". just remember that they might've been burned by a petowner before so they might be a bit nervous and being as flexible as possible might help change their view.
Also, whenever our tenents move out (or we aquire another property), I am DEFINITELY going to suggest to my husband/inlaws who we own the property with that we should get "pet references". That's a BRILLIANT idea!!
RE the 6 month thing - our tenent is on a 6 month lease but we had to decide when we started if we wanted a 6 month or 1 year lease and we weighed the options for us taking risks into consideration etc. (as this was our first rental property), so I know it's obviously out there to have 1 year leases but as others have pointed out, it might be due to credit (or lack of) in the UK with people on this forum or they just happen to be picking 6-month leases ?