Well, yes you can grow them - a well-lit conservatory or a greenhouse will be needed - and you need properly harvested seeds from fruit that have been allowed to ripen while still on the vines, and a variety that has been developed to produce well in home-growing conditions in the UK.
Lots of info here http://www.rhs.org.uk/Gardening/Grow-Your-Own/Veg-A-to-Z/Peppers-including-chillies
If you've got the right sort of place why not pop into a garden centre next spring and buy two or three seedling plants to start with - then you can pot them on and get used to what sort of care they need - then if you've been successful with harvesting some fruit, then the following year if you've still got the 'Pepper Bug' you can buy some suitable seeds and get sowing
I don't have a conservatory or greenhouse so I bought some chilli plants this spring and grew them on in pots on my patio - brilliant - will do it again next year. Bell peppers can be moved outside into a sheltered spot if we're lucky with the summer again next year, once the weather has warmed up