'Fell' isn't a synonym of hill, and it's more restricted than simply 'UK'. In some cases, a closer synonym of 'fell' would be 'moor'.
Here's the dictionary definition of 'moor':
: [in Britain] a tract of open uncultivated upland, typically covered with heather.
However, whereas 'moor' is used throughout the UK, 'fell' is only used in specific locations. You'll only come across this word in northern England, and occasionally a few places names in Scotland. Nearly all the places referred to as 'fells' are in the Pennine region (Lancashire/Yorkshire) and the Lake District (Cumbria). It can refer to a whole stretch of moorland or a specific peak within a moorland area.
If you google image some of the place names including 'fell', you'll get some idea of what kind of places they are - high and fairly barren, with rough and sparse vegetation. Sheep grazing is practically the only use you can put this land to, plus a certain amount of tourism. The fells of northern England are popular with walkers, and there's even the sport of 'fell running' for the fit and hardy.
The term is never used in central, southern, western England or in Wales. I know it because I'm from the north and am familiar with its geography, but the average Londoner with no interest in the countryside may well not even know what a 'fell' is.