In terms of getting around your dh...
Last year, while we were on holiday (and I was cycling another bike with a standard child seat on the back) dh had gone to pack the car and I was left to get me, dd and ds and the bike to the car park. Dd (who was 4 then) walked next to me and I put ds (then 2) in the child seat of the bike and I pushed the bike. At one stage, there was a downhill bit so dd ran and I cycled slowly. When we got to the bottom, dd fell and instinctively (you may say stupidly!!) I jumped off the bike and completely forgot about ds and the bike tipped backwards (the child on the bike wrecks the weight so if you let go when you are not on, quite often the bike will flip over).
Luckily he had his helmet on but also, he realised what was happening and sat forwards. He didn't hurt himself at all but it did make me realise that basically, those child seats are only a bit of plastic. They are not going to 'save' your child if you crash into a car BUT the way they are built- if all you do is crash into the pavement and your child is properly strapped in, then the plastic bit will certainly save them from hitting the pavement/road.
Honestly, with your child on the back, you become extra cautious anyway. I would advise you to try it out in the park a few times before you venture on the road - also, if you are new to cycling and in London, you can get cycling maps from the mayor's office (or through your council) which highlight quieter roads or off-road cycle lanes.
You will love it, it's great exercise (only way I've lost weight!) and your baby will love it too!