We had a very straight forward flat buying, first time buyers, no chain, no one backed out, and it still took 3 months 3 weeks from the offer being accepted to completion. We were told several times by the estate agent, solicitors, and building manager that was nearly a record. We were lucky, the previous buyer backed out and it came back on the market right as we were looking! The flat we were renting, we bought because our landlord was selling, was on the market for over 7 months before it received a viable offer. It'll still probably take another 2 - 3 minimum to complete on it even though it's vacant and has no onward chain.
If your husband has no offer on his flat yet, never mind a date of exchange or completion, I'd seriously consider moving without your animals if you can, sorting through the housing situation and jobs, and moving them over at a later date. We had to do this when I first moved. The move and finding a flat and job was so stressful on me I missed my cat's paperwork date. I moved over to stay on my visa track, kitty stay with my mother and moved over a few months later once everything had calmed down.
