Food/would, tear/prayer, and broad/reward (among others) may or may not rhyme depending on the dialect of English you speak. Britain/written should rhyme (first vowel is short i, second is schwa, I can't see any variation there), although... heh. I think I know why they may not to mc.
See, many North Americans (I don't, but my mother was British and I'm weird) turn "t" sounds found between two vowels into "d" sounds. This might sound weird, but try it, with words like "later", "eaten", "Saturday", etc., and pay close attention to what sound you actually pronounce. "written" is of course one such word. (the double t means nothing! Stupid English!) Now, notably, British English-speakers never do this, so all I can think is that when some people say the word "Britain", they take on a slight British accent just for that word, and keep the "t" sound as, well, a "t".
