No it's not ok for you to pay her cash in hand. It's illegal. If you get caught you will be liable to paying back tax and NI and a large fine, I think it is around £10k and/or a prison sentence.
You might think it's ok, how will they find out, but people talk, social media is every where, there have also been nannies and employers on mumsnet who say I do it cash in hand, you might think it's anonymous but you can be found.
A nanny friend of mine was part paid cash in hand, about a fifth of her pay, when she quit her job, giving the correct amount of notice etc, her boss was so pissed off that she told prospective employers calling for a reference, that the nanny had bitten her child and she had fired her, so the nanny called HMRC, told them that they had paid cash in hand for 3 years, HMRC went through all of the nannies bank statements and the ex-employer had to pay back taxes on all the cash in hand, plus on a lot of kitty money that she had given the nanny by cheque but had no proof that this was kitty money so HMRC said it was overtime pay, they ended up paying over £10k and a £3k fine on top, if you can afford that, then go ahead!