What an awful thing to ask, "have you just arrived in the UK?" :(
Anyhow, wow! You must be chuffed. This did actually happen to me about 6 years ago. There were quite a few cases of it, and it was well publicised. Unfortunately, it was an error, and I had to give it all back (a very similar amount to yourself) six months later. I did phone them, although I did umm and arhh about doing so.
You will never get away with anything when it comes to the Inland Rev. If they make an error, they will soon realise and expect you to pay it back. If you haven't informed them, then you could find yourself in hot bother.
Given my personal experience, I would always advice to phone them straight away, before you even think about transferring it into a savings account.
However, in this case it is obviously correct and it must be some kind of underpayment. What a result! :)
To the person who said it was sponging. Working tax credits are based on your income. If you have a low income, then you get it topped up by the state. I hardly think this is "sponging", as you only get it if you work. Bit harsh, in my opinion.