16 hours per week, 832 hours per year (give or take), £500 per month, £6000 per year
£7.21 ish per hour.
I am assuming £500 per month is Gross pay (as I always do when it isn't otherwise stated). As it is a part-time job, it is very important to you as the employer to agree the wage Gross, as the nannies personal tax allowance MAY NOT be allocated to your job.
£7.21 per hour is above National Minimum Wage, so it meets the legal requirement. I have had a full-time job paying a similar amount in the past, but part-time jobs do tend to pay more - as the person needs to find other work to fit around your job, if they require full-time work.
You want the 2-days to change? I would doubt that many people would be able to accommodate that. You will need to look for someone who only wants a couple of days work, not someone who wants to patch together two part-time jobs.
Salary wise, you may be able to get someone just out of college / just starting out nannying at that level - though if you need someone with prior experience then I would expect salary will need to go up a bit, probably around £8 Gross per hour.
Have you looked at other jobs in your area? It can be useful to search nanny adverts (at NannyJob.co.uk) to see what other employers are offering.
There is a job being advertised in Stourbridge for example... 4-days a week for £5.43 Net per hour. If I do Net to Gross salary based on usual tax code thus assuming they have no other jobs... then it's around £16220 per year Gross, which is £6.78 per hour Gross. Thus not dissimilar to your £7.21.
I think you can give it a go at that salary figure, then adjust the salary as necessary to obtain a suitable candidate. I do however feel you need to FIX the two days.