What you probably need if you're looking long term and you don't want a cash bank account is a basic, no-frills index tracker with low fees and that will accept a low monthly investment.
Good ones that I know of include M&G UK index tracker fund, and Fidelity Moneybuilder UK index tracker fund. Both are cheap (ie. have no initial charge and low annual charges) and have reliable admin.
Index trackers are pretty much of a muchness wrt performance since they track the index (either FTSE 100, ie. big companies, or FTSE all-share, which is what we have). The main variable is fees, so it's important to check that out.
If you want something slightly racier, you can go for a global growth investment trust fund, which also have lowish charges. Witan is a reliable solid performer in this sector (managed by Henderson) and they have a specially branded children's investment option called (iirc) Jump.
But overall you shouldn't be seduced by packaged children's funds, since it's just wrapping and what matters is what's inside. Make sure when you fill the forms in that you do it as a bare trust so that it won't count towards your taxable income. There's usually a box to tick and a place where you fill in the initials of a designation, which means that although you legally own the investment, the child is the beneficiary and the money is earmarked for him/her.
hth