How awful 
Difficult to say anything if you cant prove it but
at anyone who would still £ from a childs piggy bank

And should you get any sort of proof than no way should you let her stay another minute. Id sack immediately for gross misconduct and write the most basic of basic references. "Nanny worked for me from X to Y, looking after my DC called A and B aged X and Y I would be very happy to talk to you, please call me on this number"
Im assuming you can write that legally?
If i had proof id also go to the police. Theft is theft regardless and it would be nice if it being on her CRB stopped her working for anyone else, or via any agency etc etc.
Also Im assuming she has definitley stolen it..... thinking about a few times when i had no change for car parking and genuinely borrowed a few silver coins from charges piggy bank. always gave it back within days, and wrote in nanny diary that I had borrowed a few coins, or perhaps changed a £2 coin for silver coins from his money box..... and and ASKED my 3 / 4 / 5 / 6 year old charge, and explained etc etc.
(so had MB or DB realised it was £2 short, for 24 hours or so, even if they hadnt read the nanny diary, their child would have been able to say that we borrowed it, and that HE put the coins in the parking meter etc etc)