Thanks for the recommendations, everyone!
We are trying to find a cot rather than a cotbed due to issues with space. Our house is 2 bedrooms now but the spare room is two floors away from the master bedroom, and I don't feel comfortable having a child sleep that far away...it's just a really awkward set up, with the kitchen and living room not even on the same floor as the spare room (and we're holding off on moving because we may be moving back to the US when the baby would be somewhere between 15 and 18 months). A cotbed is just too big to fit into our room but the cot dimensons we've seen would work...and I'm hoping we can just keep the baby in our room until we know one way or the other whether we're going back to the US or staying in the UK.
We haven't gone into Mothercare yet but will check that out this weekend. I really liked the cots we saw at Mamas and Papas but hated their mattresses and the cot I liked the best was slightly bigger than the standard cot size, so we'd have to go with their mattress for that one, I think? I think it's the mattress search that has been the most frustrating. That Mothercare mattress is more along the lines of what I had in mind (breathability is important since our bedroom is on the third floor and can get stuffy). This shouldn't be such a BIG DEAL but pregnancy hormones combined with dealing with a huge leak from our shower to our kitchen that our rental company still has not addressed after 4 days (!) combined with general frustration over the space issue has just left me overreacting to even the smallest things.