CTFs were available to children born from 1 September 2002 to 3 January 2011. As she was born in this period she will have a CTF and won't be eligible for a junior ISA.
You can speak with the child's parents to find out which CTF your great granddaughter has and how much is currently being contributed to it on her behalf. Part of the benefi ts of a CTF is that friends and family are able to contribute to them. Up to £3,600 can be invested in total each year.
If the full amount isn't already being invested, you could consider putting your money into the fund. The money will earn interest tax-free until she turns 18, when she will be able to access it and spend it as she wishes.
There are also other options you could consider, depending on whether you want to invest money for your great grandchild's future or simply save money into a cash account. If you would prefer the latter, you could open a children's savings account.
Children's savings accounts belong to the child, and are taxed as the child's unless interest on money given by parents exceeds £100 each year per parent, in which case the liability falls back to the parents.
There are no such stipulations for money given by grandparents or great grandparents so you should be able to take advantage of the child's personal tax allowance of £7,475 (2011/12), which for most children will mean there will be no tax to pay on interest earned.
However, while a savings account may suit a cautious investor, it is unlikely to be the most profitable way to save for a child's future over a long-term period of, say, 10 years. A fund investment is a better long-term option as the returns are likely to be larger. This can be set up to take either one-off or regular payments.