Have a look at
http://www.british-blc.com/academy2/...c%20chart.html which lists 44 words together with their phonemic symbol. The chart also highlights the portion of each word that relates to the symbol. You can also listen to the pronunciation of the word together with the portion of the word that relates to the symbol.
The Oxford Advanced Learner's Dictionary uses these phonemic symbols to indicate pronunciation. The dictionary also differentiates between British English and North American English. The dictionary further lists three additional symbols for the following sounds: 'y' as in 'many'; 'u' as in 'actual' and 'o' as in 'go'. For an audio rendition of these three words you could try Mirriam-Webster Online.
So, adding the British Language Centre's forty four sounds to Oxford's additional 3 sounds, you have a total of forty seven sounds.
I am no expert, but apart from intonations, I would suggest that if one were to learn the correct pronunciation of the 47 words depicted, one would have the basic building blocks to pronounce any word in the English language.