Xena - are you new on MN? There is a Xenia who posts on here whose name (and whose very forthright views) are, umm, very well known. Your name might confuse a few posters....
Anyway you will find it a problem because HMRC always assume either weekly or fortnightly, and the official tax tables are not geared to anything else - so a nanny agency will not be able to do fortnightly payslips because the data they need is all provided by the government. And wheras the fortngihtly calculations themselves can be easily produced on a spreadsheet by anyone with a reasonable grasp of PAYE, it won't help because at year end the agency has to document everything on official HMRC forms (or electronically) which cannot accomodate this, so it becomes a real fudge, and I suspect that no nanny agency will be happy to do this for you.
Simple way round is to contract your nanny to be paid monthly, but add a clause in your contract as follows:-
Although (X) will be paid on a monthly basis, an amount of half the monthly net wage will be pre-paid to the nanny on the 15th of each month (and will be deducted from the month-end payment). Effectively therefore, the nanny will receive half their monthly pay in advance each month. This clause is at the sole discretion of the employer, and can be revoked at any time.
Then you treat it as a normal monthly contract as far as the PAYE/tax companies are concerned
No recommendaitons for any of these tax companies - I find it easier to do it myself. HMRC are very helpful if you choose to go down this route...