Most of the banks have savings a/c for kids - just log onto their sites to see what offers they have. Also, don't forget the post office & credit unions too.
If you search/browse this forum and the Savings & Investments forum you will find many threads dealing with this specific issue of recommended savings/investments accounts/products for children (e.g. Child Benefit).
Well our one month old just got his PPSN in the post this morning. However he doesn't have a passport or drivers license yet nor does he pay any of the household bills (sponger!). I presume that a parent/guardian can satisfy the money laundering rules on behalf of a dependent child?