It depends on age and experience of the nanny. I work in SW London and nannies I know earn between £8:50 and £11:50 net per hour (£10.42 and £14.83 gross) work out what you can afford to pay gross, including employers NI (£61 per week based on £14.83 per hour) then take off a £1, then you can haggle with someone you like! Offer a pay review in 6 months or afford a pay rise after a year, afford birthday/Christmas presents, a box of chocs/bunch of flowers occasionally to show your appreciation, afford any over time (bus/train delays) always deal in gross wage with you prospective nannies but work out the net weekly wage for them.
Also remember there are other expenses in employing a nanny. Heating during the day, feeding the nanny (most nannies get lunch, tea, coffee, biscuits, snacks, some have breakfast and or dinner as well!) kitty for classes, swimming, farm, zoo, the odd visit to Starbucks! You will need to provide craft items and baking ingredients (if you want your nanny to do those with your children)
There shouldn't be any problem finding someone to do 3 or 4 days a week but if she has another job, the net amount she will take home from you will be significantly less as she will have used up her tax code in the other job.
I do the odd housework type thing, I will unload the dishwasher, empty the bin when it's full, sweep/mop the kitchen floor if it is needed, Hoover the areas the children use, playroom/sitting room/ their bedrooms, I will do all the children's washing and ironing, cook and batch cook for the freezer and make extra for my employers on occasion, dust their bedrooms. I will take my employers washing out of the washing machine, fold from the dryer (I will not match socks or unravel washed socks!!) but that is it on their cleaning. I will run errands (drop/collect dry cleaning, collect parcels, post/return parcels pick up bread/milk etc for them if we are passing a shop) and will do the family on-line shop from their shopping list and add stuff for the children/me.
I have found 8 out of 9 of my positions through agencies and one through the local paper. I have looked at Gumtree and Nannyjob but I have never had any luck through those. I found my current position through Wimbledon nannies, who are lovely and really do try to match family and nanny.
Good luck!