Oh, what a mixed bag. I think you need more information. The flat in Knightsbridge is not to be underestimated and I expect is worth a whole lot more than £400 per week on the open market. And then of course there is food, tel, etc. which I assume is thrown in.
Those hours are long. And the ages of the children are hard work... especially if they have another. But, I think £350 net for what is effectively your disposable inclome is not bad.
But... I am worried about this listen out for baby because it would be upsetting for them to see parents in the morning. Eh? My children would be upset not to see me in the morning (and likewise!). In fact I have on occassion had nannies who wanted to let them sleep in during the hols and I said no as a general rule because I WANT to see my kids before i go to work. As a one off if the kids are out late a party or something, okay. But, not all summer long. Forget that.
Also, whist basement flat sounds cool, I can't helpo but wonder if this means you have the maid's/butler's room off the kitchen. I am picturing Upstairs Downstairs and think you may have Hudson's room. So now, where does the baby sleep. I assume not in the basement with you... and so how would you "listen out" for him/her? Have you seen this house? I would want to know more about where I am to spend my time and where the children spend theirs. Will you be allowed to use the front door? Do they have other servants (either live-in or live-out)... a maid perhaps?
And what is meant by "light housekeeping"?
For you, you said you have 4 years of experience. Is this live-in full time nanny to young children? Nursery work? Babysitting?
My concern on this job is that it is an awful lot of work. Three nights of babysitting is probably too much. Oh, and are three nights restricted to mid week (Mon-Thurs)?
I'm sorry I have asked a million questions. But I think you should think about what kind of employer you want to work for / live with. Some pay out lots of money, treat you like a servant and expect you to know your place (downstairs). Other can probably not offer such a comfortable pay package but welcome you in to their whole home, and treat you more like a member of the family. And of course, there are wealthy people who do both of these things.
Maybe I have extrapolated way too much out of the basement flat in Knightsbridge. But, I think you should be clear on these expectations (if you are not already) before you accept this job.
Oh, and I absolutely agree that you either start at 6:30 or you start at 7:00. And your time is your own until such time you have officially begun work.