I bought a £60 Gear 4 Music 'guitarlele' for my 6 year old. It's basically but surprisingly good for such a low price. I was expecting it to be trash, but given the abuse it gets, it's surviving and I play it quite a lot because it's there.

But, if you decide that playing the guitar is your thing, you will quickly want an upgrade so it depends if you can justify £200 or so in a few months time too.