No idea about cheshire area as such but i imagine you could get a nanny for 4 days that would cost you about (maybe slightly (a FEW £)more) than £400 gross per week.
Givent that nannies odten do a 10+ hour day many of us LIKE a 4 day week (i work a 4 day week, and love my 3 day weekends!)
make sure you always deal in gross figures when employing a nanny!
i recommend nannyjob or gumtree as well, as most nannies search on there when looking for work and it saves you an enourmouse agency fee that is around (occasionaly more than £1000 , daylight robbery IMO!)
so long as you check references yourself (which any sensible parent would surely do) and check that they have a recent crb and 1st aid certificate that should be fine.
If your nanny is 'approved' (costs about £100 + 1st aid course if she doesnt already have one) then u can use childcare vouchers to pay part of her salary, and save yourself some NI. (your NI, NOT your nannies NI, which as her employer you will be responsible for collecting on behalf of her and passing onto inland rev)
I expect you know you will have to be her employer and provide a contract, wage slips, and a minimum of 4 weeks holiday per year!
Good luck!