Agencies don't really work for au pairs.
Most people recruit successfully from au pair world. You put a profile on with your requirements and lots of nice smiley pictures of your family (I read lots of other people's first and then extracted the phrases I liked). You want to make a big thing of the flat, but also that you want someone independent.
If you need a driver, you'll want someone over 22, who has had their licence for at least 3 years (or insurance is impossible).
You also want to make sure they have a police check, a copy of driving licence (check for endorsements), and passport copy to check immigration status. I also ask for a reference. I sometimes ask for a doctors note to check they're fit and healthy.
It can sometimes take a bit of time to get everything ready, so the other option in London is to get someone on their second au pair job, who is already here. For that, you advertise on gumtree or on one of the au pair in London Facebook pages.
The advantage of that is that they will have a reference that you can check from their previous host family and also a bit of experience.
The disadvantage, is that they may have set ideas on how integrated they will be into your family. For example we don't often take our au pair out with us at the weekend (often as we either see our friends, or do very boring child related activities). Some do, but not that many, so its important to get their expectations correct before they start with you.
Hope it goes well