I would put it on the market now, it is taking much longer to get mortgages due to the rules, even for first time/cash buyers. Plus getting your chain started could put you in a favourable position, and accept you are likely to be moving with a newborn. Spring is fast approaching so you may find you see something you like and haven't moved fast enought.
I agree you should put it on the market now as the market tends to be more active at this time of year.
Your flat will seem less cramped if you are selling before the baby is born than if you have baby and toddler stuff around the place. You will also have an incentive to find somewhere and something to push your buyers along with if you are selling and looking to buy before the baby is born!
DC1 due in May, I think it would be best to market the flat and do viewings without a tiny newborn! I want to put the house on in March/April to complete in May.
DH wants to do one thing at a time and plan it so we can move in Aug, but then we'll have to keep the tiny flat tidy with a newborn, and have viewings and stuff with a new baby! We have a major storage issue in this flat and I'm sure that will be accentuated with loads of new baby stuff around.
Reading your replies so far I definitely think I'm right