Your location could make a difference to your chances of finding someone. I think you used to live in Greenwich (I seem to remember seeing your username in the past - I grew up in Greenwich area thus read threads to do with Greenwich on occasion) but you moved about a year ago... did you end up staying in London?
As a nanny, I would not be interested in a 3 day job which involved a Saturday. When I was younger perhaps but a 3-day job just doesn't tend to pay enough to cover the mortgage and other bills. 4-days a week does... and I quite like working 4 days a week, much nicer than 5 days.
However not all nannies are like me... some won't mind working 3-days one being a Saturday... though be prepared for it not appealing to many. Try advertising for it... see what you get. Then if you don't get suitable applicants, consider what other day combinations could be possible.
Remember to agree a GROSS salary... as the person could have another job which may already be using their personal tax allowance.
I would avoid a nannyshare if I were you... you have a 2 year old and will have newborn twins. The last thing I expect you will want is any more children in your home!
It isn't clear if you will be working away from home whilst the nanny is caring for your children. Some nannies can prefer to have sole-charge and may not work that well with a parent around at home all the time. Others will be fine with it. If you specify it in adverts, then applicants know from the start if the job is working alongside you, or if it's sole charge.
Have you seen my Example Costs of Employing A Nanny post I did back in December? Could be useful reading as it talks about salary and many of the additions on top.