As with all savings accounts, the deals change all the time and you have to keep an eye on them constantly, so this can't be a definitive answer. But at present, children's Isas are looking like the best bet (a children's trust fund is good too, but these have now closed for the present). A Junior Investment Isa can be opened for a monthly investment of as little as £10, or a lump sum of £750. You can put in up to £3,600 a year and the account is valid until your child reaches the age of 16, but they can only access it after they are 18.
You could also check out this list of recommended children's accounts. Some of these offer very good rates of interest - 5% on the Future Builder - but all these offers should be checked carefully because very often, a good offer is only valid for the first year and you have to keep moving your money to get a good return. You may like to seek some professional advice before investing a lot in one of these accounts.