We don't use the term redneck in Britain except when discussing North America. There isn't an exact equivalent in British English. We would perhaps call unsophisticated country people bumpkins (or country bumpkins) or yokels, but these are pejorative terms, and country-dwellers don't identify themselves by them, except ironically. The words hick and hillbilly are used too (also pejoratively) but not very often. None of these terms evokes the likely political views of this group of people.
If we want to stress people with conservative, traditional views we might use the collective term Middle England, but this group of people are almost overwhelmingly middle class. Little Englander is very occasionally heard or seen. This was originally a historical epithet - it described someone who was against Britain's imperialist pretensions. Now it refers to someone who is very insular, is unenthusiastic about the European Union or any other international organisation, and is generally uninterested in other parts of the world and their inhabitants.
There is the relatively recent word chav, but that refers to a certain look more than anything else (the fashion labels Burberry and Kappa are associated with chav culture, as are huge hooped earrings and hair scraped-back into a pony-tail for women). I doubt that many chavs vote. It is a pejorative term, as is its synonym pikey, which rarely appears in the press, as it is a contemptuous word for a gypsy. It is therefore seen as politically incorrect to use the word.
The term provincial gets across the rural sense and the narrow-mindedness that is perhaps suggested by the word redneck. It is both an adjective and noun. The adjective parochial could be used too. Neither word is as pithy or picturesque as redneck.
The countryside in England has always been seen as rather posh. Fox-hunting was always the preserve of the upper classes. That may be why there is no British English equivalent of the term redneck. There is a Scottish word heuchter-teuchter or heuchter-cheuchter, which is what city dwellers historically called Highlanders. It's a rare word (in England, anyway) but an internet search suggests it's used in a positive sense. The Irish equivalent is culchie.