From the perspective of a nanny you are on a very low wage, but you were happy with it at the time and a pay rise isn't essential, it is rather a luxury some nannies seem to have. In some jobs I received no pay rise, asked and was declined. This job I got a 2% after one year, presents, no Christmas bonus. I started out young on £8 gross but those were temporary jobs and for experience not as a nanny career job if that makes sense.
I am central London and every single nanny I know that is Live out is on a minimum of £10 net, some with no qualifications but solid nanny experience. I know a few foreign nannies who are paid cash in hand but that's another story. Some families in this area do pay £9 net but thats rare. It is true the going rate is £10-£12 net in this area, I know few nannies on the £12net, one is on £13net, gets a month Christmas Bonus, amazing presents, but she works her socks off and mum doesn't work (think micro managing). You just have to weigh up what sort of family you want to work for, your attitude to the job, how comfortable you feel starting afresh with new demands. Also factor in your commute cost and travel times.
What I would actually suggest you say to your employers is this: "I am struggling financially, and as I am getting older I see nannying as my career and need to make some serious decisions as to my financial future. I would like to save for a home etc" I would then say "I feel that at my current pay I cannot do any of these things and I wanted to let you know my concerns and was wondering if you and your DH could discuss what you can afford"
Ultimately this gives them the option to say ok we really value you and can stretch to this, or actually we cannot afford any pay increase. After a long time in the job you should be comfortable enough to have a grown up decision, they will also realise that you probably will leave if you don't get a raise.
Also after three years your current employers should happily give you a reference regardless of whether your leaving for more money or not. Being a nanny is a job and people move jobs for money reasons all the time!