Ok, having read all the comments so far, I feel some things need to be cleared up.
Nanny Tax and NIcs
Nannies are like any other employeee, the employer deducts Income Tax and National Insurance Contributions from the employees Gross Pay, paying the employee their NET take home pay and paying the deducted amounts to HM Revenue & Customs. Employers also pay Employers National Insurance Contributions, if paying their employee above a certain threshold.
For a 2 day per week nanny, I would expect that you can use Simplified PAYE (2007)
Working from home, with someone else in the home caring for children can work... but it can also be difficult. Noise in my view is a big difficulty (used to work for a parent who made international phone calls from their home office). It does have it's plus points though, you don't travel to work... you can spend your lunch break with your ds, etc.
However, two young children in my view will soon become two active toddlers, then two very active pre-schoolers. With good routines, children can spend a lot of time out of the home - going to local groups, playing in the local park, exploring local area, etc.
With regard to salary, my general view is that a nanny will cost about the same as two children attending a childminder. As mogs wrote, she charges £5.50 per child as a childminder, whereas a nanny will cost £7p/h gross to £10p/h gross and possibly more (though also possibly less if you can find someone prepared to accept a lower wage). As several of us on this board always write when talking about wages - ALWAYS AGREE A GROSS WAGE, NEVER NET. This applies especially for part-time employees, as you don't know what other work they may have.
If budget is a bit on the low side, ask your employer about Childcare Vouchers - as many childcare providers (including some nannies) can accept these.
With regard to working from home, check local planning rules regarding a home office and also look into how it may affect things such as Council Tax .
As you are only wanting a maximum of two days per week, and as you only have one child... I would suggest considering the nursery (and childminder if you can find one) options. While there may be some hassle in taking you child and picking them up again, you don't have the responsibilities of being an employer and you don't have someone else (or in this specific case two other people) in your home.