I know (as a Briton) that Britain was involved in the War before America and were fighting the Germans and the Japanese quite early on, but how come we never hear stories of British troops fighting, and British WW2 battles are rarely shown in film or media, so why is this?
Films are commercial projects made by studios. The American movie market has historically been the largest and rightly or wrongly the studios believed that more Americans would see movies about Americans rather than Brits. So, you have a movie like The Great Escape which shoehorned Americans into a British escape, or U-571 which turned one of the Royal Navy's greatest accomplishments (capturing the enigma machine) into an American operation.
British valor in WWII has been featured in many high profile projects. For film, I would recommend The Longest Day (1962). The cast is incredible, and the history is pretty good. It features long segments of British troops, and is a classic in my opinion. In a similar vein, A Bridge too Far (1977) is excellent, and shows the gallant but doomed efforts of British paratroopers in Operation Market Garden. It also highlights the difficulties of British armor in attempting to relieve the paratroopers. This is another WWII classic movie. The book Pegasus Bridge, by the problematic but popular Stephen Ambrose, is an excellent description of a brave assault on and defense of a vital bridge on the extreme right flank of the D-Day landings. Bridge on the River Kwai (1957) has major historical problems in its narrative, but is popular nonetheless. Each of these are quite popular representations of British WWII accomplishments. There are others as well.
Any answers I could give as to why the British efforts in WWII are relatively less featured would be speculation.