For a first time mum, I agree with the other posters that a Norland nanny is the safest route to take especially with a young baby. They are career nannies with the proper training behind them, and there are a lot of them here in London so they are highly networked.
There is a pricing structure depending on the nanny's experience, so depending on your budget you can get a Newly Qualified Nanny (NQN) who has just completed the Norland 3-year course or a Fully Qualified Nanny (FQN) who has graduated from the college. Their rates go up with each year of experience they attain. So a nanny with 6 years experience will be a lot more expensive than a nanny with two years experience (which makes sense). They can either be live-in (which would keep your costs down) or live-out. The agency website has the pricing structure so you can familiarise yourself accordingly.
Do contact the Norland Agency
https://www.norland.ac.uk/norland-agency and have a chat with them about what suits you and your situation best.
Note, NQNs get snapped up fast so there's no guarantee that you'll get one.