I would suggest your next best option after stocks and shares would be a mutual fund that tracks a major benchmark bond index. Look for something with a low MER (definitely below 1%, hopefully around 0.50%). I am not specifically recommending this mutual fund, particularly because you are not in Canada, but something like the TD Canadian Bond Index fund would be worth considering. There will be British alternatives. You could hope to see somewhere around 5 - 6% annual growth, so it's not going to make your daughter rich (don't forget, there's inflation that'll eat away at your savings). That return is, of course, not guaranteed and you may actually lose money.
If bonds are too much risk for you, you need to look at a money-market mutual fund. You will generally see returns slightly higher than a savings account but lower than a bond-index mutual fund. The risks are only a tiny bit higher than a savings account (but the interest is also only slightly higher).
Before you take this advice, wait until someone in the UK posts about investment opportunities similar to Canada's education savings plan. In Canada, the government will match some part of your contribution, and the money can compound tax-free. I'm not sure what similar options are available in the U.K., if any.