I think many nannies seem underpaid because they talk net. Earning £350 a week for them is £500 for most people.
Au pairs are a completely different kettle of fish - they get a lower wage (reflecting their lower experience and qualifications) but do get room, board, food etc and typically work fewer hours.
Likewise childminders charge per child per hour or per day, so may in fact be earning £15/hour by maxing out their spaces but each child pays £3/hour.
So depending what solution you want for, say, a 20 hour week you could pay £60 plus living costs of an au pair, on average £80 for a childminder or £120-300 for a nanny.