Looking at my recent photos just now it was revealed to me once again that my current camera is rubbish and takes rubbish photos (a Fuji A850, don't buy it)
I need a camera that is relatively simple and inexpensive (preferably under 100 British Pounds but it can be a bit more). I don't want anything special just a camera that takes great photos during the day, okay photos in darker environments (that's one thing that annoys me about my current camera, apart from when it's bright daylight all the photos come out fuzzy) and has a simple video function. If there is anything else I should consider please tell me.
Advice from anyone is welcome but I just want to note that I live in the UK.
Though what you ask for seems simple, technically it requires quite good components, hence costs quite a bit of money. Almost nothing but a digital SLR will take indoor photos well without a flash, and nighttime photos without a flash require a tripod or very good camera.
As INTP said, cheap compact cameras are normally rubbish. If you want to look through your options,
DPReview (which someone linked already) isn't a bad site. It will at least give you an idea of what is around and the quality difference.
The main things you'll care about for low-light photos are the sensor size, megapixels and minimum F number. For the same sensor size, less megapixels is generally better. This seems counter-intuitive but larger pixel size=higher signal-to-noise ratio, so an 8 megapixel camera can be significantly better than a 14 megapixel one. If I was buying a camera of any type, the first thing I'd look at would be the lens quality also. Some of the cheap ones will have pretty poor lenses and quite soft/unappealing photos as a result. For some reason people forget how vital the lens is when they buy compact digital cameras. Good image stabilisation (anti-shake) can help in low-light also, but only to a point.
After saying all that there will probably be something that will satisfy you for a bit above your price range, say 150 pounds, so check out the suggestions people make on here. I like the panasonics, but I own a panasonic so have a bias. The canon compacts have better colour than the panasonics, the panasonics have Leica lenses that make many of the canon photos seem soft by comparison. Canons also seem to overdo the noise reduction. What it really comes down to is which camera you like the photos from the best. So sample photos are a good way to choose.
Last thing I'll say is that it comes down to how you use a camera as well as which one you choose, so getting a camera with some manual settings and learning to use them quickly can improve photos significantly, especially in lower light. Sorry if it seems complicated. The fact there is no simple solution annoys me too; physics can be limiting sometimes.