^"A 2 bed semi in London is not really adequate housing for a family of four. Why on earth have you just moved into a 2 bed house with one child, and another on the way?
And yes, do apologise. She is probably also really worried about her future in her home, as you are unable to settle one child, and soon there will be another in this restricted space."^
Then maybe OP should use her crock of gold to move to her detatched farmhouse over rainbow with surrounded by two acres of adjoining farmland.
A 2 bedroom house is perfectly adequate for 2 adults, a toddler and a baby.
Saying: "as 'YOU' are unable to settle" is probably why she is so upset in the first place. Your baby cries and the world looks at you with judgeypants hooked over ears like you are the worst mother in the world because you can't stop your baby crying. IT IS WHAT THEY DO. Maybe the neighbour has some suggestions for keeping baby quiet? Duct tape perhaps?
That said, don't upset the neighbours, see if you can manipulate sleeping arrangements, apologise, see GP, get DH to take some shifts, but you are a bit stuck. If OP whips downstairs at the first opportunity with DC, DC is going to be thrilled and wake up every night for play time from now until 12 years old. You must be feeling haggard OP, preg+sleep deprived ouch. Though it feels like it, your neighbour doesn't assume that you are sleeping like a log whilst she is being kept awake. But it is your baby, not hers.
DS1 woke up frequently from around 9-18 months, up to hourly, stopped eventually,but yes, some tears needed to be shed for it to stop. DS2 is going to be a trauma as well, but at 4 months and co sleeping on the boob (WHAT HAVE I BECOME-SOBS), the only person in our house (indeed entire block of apartments) is ME! Honestly, will get beter OP, try not to let neighbours stress you more than you already are, once you explain, they may be a little more understanding?