Hi,
We run "The English School at the Chelsea Centre" at the World's End in Chelsea (if you put that through google, you will come straight to our website). The times of our morning classes and part-time options are designed for the needs of au pairs, of whom there are many around our area. If you are in Chelsea or within travelling distance, we are always interested in finding homestay accommodation for our students, which could include some babysitting in return for reduced price or free accommodation.
Although you may find schools in your area willing to help you, schools do not run reference or police checks and so you would need to do so yourself, especially if your help will be in charge of your baby when you are not around.
Alternatively, you could advertise for an part-time au pair and offer to fund a suitable course. This is probably the better option, as an au pair agency will run checks for you and be experienced in dealing with any problems that may arise - schools will probably not be able to help.
It is worth bearing in mind that if the au pairing is only part-time and the student may want to earn extra money in a part-time job, they may not be allowed to work elsewhere on an au pair visa. An EU student who has the right to work will not be tied to you financially, which may be a consideration if you are not in a position to pay a full-time rate for a part-time position.
I hope this helps and wish you good luck with finding a suitable person.