My husband and I live in central london and have hired a nanny to look after our ten month old son for 40 hrs a week at a rate of 540 (net).
Like others on here, I'd like to know some history.
When did you hire this nanny (this may be important if you do decide to end the contract)?
Why have you put the pay on here as Net? Whose idea was it to agree a Net wage, the nannies, yours and agency? (Interested to know this due to this thread about Net v Gross wages)
£540 net per week in 2010/11 tax year is £38,020 Gross per year. £42,155 cost to employer.
That is £18.25 Gross per hour which is high even for Central London.
will now need our nanny to work for 48 hrs per week. She asked to be paid more for this time increase, at which point we raised her salary to 600 (net)
If calculated hourly, keeping the Gross at £18.25 then Net Weekly for 48 hours increases to £638
So she may be seeing 600 net as not being so great. However her gross hourly rate is so high to start with, she's got to realise that at some point things become unaffordable for the employer.
So 600 net for 48 hours (£17 gross per hour 2010/11, £16.89 per hour, I think, from April 2011) is what you feel you can afford to pay. It's therefore up to her to decide if she wishes to accept that, or leave the employment.
returning to a 40 hr week as of May.
I think that takes it to £20.26 per hour Gross. Not totally sure, as not sure the tax calculator I'm using is doing the full calculation with the 2011/12 tax code yet.
So lets backtrack a bit... you were paying £18.25 gross per hour, for 40 hours. From May 2011 you will pay £20.26 gross per hour.
So that's an 11% rise.
She has come back to us very upset
Unless my figures are wrong (they might be, has anyone else concluded the same?) then it's an 11% rise come May and she's upset 
I just can't believe I am going to have to fire her!
I don't think you can. What you are doing is changing the terms of the contract. She can accept the new terms or not. If she chooses not to do so, then you give notice under the terms of contract and she leaves (either immediately with pay in lieu of notice, or she works during the notice period).
That is perhaps what you meant by "have to fire her" 