It doesn't matter the source of heat provided for the betta, provided that it doesn't get too cold. Nighttime temperatures certainly shouldn't dip below 18C. Besides the warmth, humidity is critical, because dry air damanges the labyrinth organ. Cold air contains less moisture, and hence is more dangerous in this respect.
Personally, I'd say keeping a betta in the average UK home is NOT advisable. The temperature fluctuations are going to be too extreme. In modern homes with good heating and insulation you might be fine, but in older houses I wouldn't risk it. If you want a coldwater aquarium, there are lots of options. I highly recommend the paradisefish Macropodus ocellaris. It's coldwater-tolerant, very colourful, and easy to keep.
Cheers, Neale