@Button moon , first, welcome to TSP. Hope you'll come visit now and then, as it sounds like you sew as well.
Thank you for wanting to get a decent machine. At 100GBP, roughly $132 USD you should be able to get a very suitable machine for a young sewist. I can't advise on a specific machine as I'm in the US and we only have a little overlap on models. But I would second a Brother, as they have decent machines in that price range. Getting one that has the variable sewing speeds and doesn't have to use the foot petal is nice and can be a lot of fun to use.
Some of the other suggestions would really vary depending on the child. I'm tall, was already 5' 3" by her age and 5' 7 1/2 by 10, so reaching the pedal was never a problem. If you need a stool or such use a wooden one and either a shelf liner or rug mat to keep it in place. Or duct tape. The hand crank suggested is an interesting option. I don't know; When little I always wanted both hands on the fabric, plus I'm left handed, so I'd have needed a designated cranker to be able to sew a stitch.
Thanks too for being willing to gamble a bit of money on a machine. I used to see women in the big sewing stores getting a super cheap/ junky machine for a child/grandchild in case they didn't like it. A junky machine is the best way to turn a child off the hobby before they even get started.
What you might consider if she lives close by and you see her on a regular basis is keep the machine at your house and work on projects together until she is competent enough and comfortable doing bobbins, threading and other basic skills. Then have her take it home if she wishes.