I wouldn't say I'm a super experienced cellist, but I did some research and got my cello on Gumtree several years back, and although I've had a few problems with it I think secondhand would be the way to go if possible.
As with anything new and affordable, especially aimed at beginners, there will be corners cut to get the instrument/bow/accessories to a 'reasonable' price, whereas a cello which has been played will hopefully have also been looked after - there's much less of a visible market for classical instruments, so I dare say the number of dodgy sellers are far fewer than with guitars and other popular 'gift' instruments around this time of year.
Unless she's quite small, you'll want a 4/4 full sized cello (maybe a 7/8 or a 3/4 if she's around 5ft and has small hands), and I'd say you'll be looking at a couple hundred pounds. As I'm sure you're aware you can spend limitless money on instruments, so not sure of your budget, but anywhere closer to a grand will get you a very nice cello secondhand although that might be excessive for a beginner.
If you do go secondhand, there are a couple of things to look out for. For the cello itself, the tuning pegs (at the head, and the tailpiece) should move freely. The bridge should be straight and perpendicular to the body of the cello. The soundpost should also be in place - if you look through the f holes there should be a post stood between the two sides of the cello, this helps the sound travel and greatly improves the tone - if it's loose, it will rattle around inside the body, and is a job for a professional luthier to fix. The bow strings should be plentiful and nice and clean, and you should be able to tension them (by turning the end) before the rod of the bow is straight. None of this should be a problem if the cello/bow have been used and looked after, I might add.
You'll ideally end up with a cello, a bow, a case, and some rosin (to apply to the bow strings) and maybe some sheet music to get her started. She might want to upgrade her bow once she gets familiar with it, but that's a whole other conversation!
Feel free to PM me with any other questions, as I'm aware this is a bit of an essay!