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I'm afraid I'm a bit of an expert on knee bandages, having gone through a fair number of them with knee injuries and joint problems. This last set was supplied by my physical therapist, but I believe they sell for around £15 each, which I find a bit excessive. Basically all this is, is a soft padded piece of elasticated tube shaped cloth. They come in different sizes, and can not be adjusted.
This is definitely a step up from the average pull on elasticated bandage. It is softer and much more comfortable as well as less binding and restrictive, while offering just a bit more support. The padding is also a real benefit if you get down on your knees for anything.
It does not, however, offer nearly so much support as a neoprene support. I have found that my knees can still give way, and this will do nothing to stop them, or a spill. It does make standing or walking less painful though, by providing some support. On the plus side it does not make you sweat and rash like neoprene can either. I have known neoprene to really rub and chaff, and at times even cause some bleeding, as well as being terribly sweaty and hot at times. Because it is all one piece, you don't have anything to come undone, but it can roll, which gets very uncomfortable.
I would recommend this to someone who is apt to be wearing knee support long term, but can make do with a bit less support then offered by the neoprene supports. Of the 3 types of support, I have found this the most comfortable to wear, and that it allows the most natural movements of the knee. This also has the advantage of forcing your own muscles to take some of the strain, which helps prevent long term muscle wastage. I also believe this support would be ideal after knee surgery, as it is soft and padded and would be far more comfortable on a cut or wound. It is soft and absorbent, as well as being somewhat breathable, which means this will be far more comfortable in warmer weather. It is machine washable, and I assume can be machine dried, but as I don't have a dryer, it goes on the radiator.
As this is available on the NHS, I expect most chemists could order one in, and help you with sizing, but of course if you can get them on prescription, that's all the better.