Ever since I began to learn bopomofo (the equivalent of the English phonetic alphabet) my pronunciation became much more accurate. With such a written system much more complex and involved than the English system it only was natural to learn an alphabet to help learn. Although I had to be diligent and dedicated to learn the new alphabet complete with new sounds associated with the letters it was well worth the time and effort. After all the letters of bopomofo are actually either derivatives of or can be found in Chinese characters. Therefore, while I learned bopomofo I was learning parts of characters for the written language.
ㄅㄆㄇㄈㄉㄊㄋㄌ
ㄍㄎㄏㄐㄑㄒㄓㄔㄕㄖ
ㄗㄘㄙㄧㄨㄩㄚㄛㄜㄝ
ㄞㄟㄠㄡㄢㄣㄤㄥㄦ
ˇ ˋ ˊ ˙
This is the complete alphabet of bopomofo and of course one must also add all the tones to this. (Five tones including the light tone.) To the untrained eye these look rather like child's musings (at least to the Westerner's Romanized brain). But once one learns this system Chinese characters begin to make more sense.
I will not attempt associate the sounds with English letters since that would negate the whole purpose of learning the new alphabet in order to free one's mind from the English pronunciation of letters. There are some very nice websites that have native speakers for each letter. Therefore, just as a baby learns by rote so we as adults can also learn by rote.
http://www.mdnkids.com/BoPoMo/
This is an excellent site that pronounces the letters as you click on them. Only letter at a time is pronounced and only in the first tone. I used this site to help know native pronunciation without falling back into the English way. It's important to learn how to shape the mouth and move the tongue so as to get the pronunciation like that of the native.
While it is still not as easy to recognize this system as it is the English alphabet, I do believe my pronunciation is better because I learned by rote. Rather than confuse a foreign language system with my mother tongue it has benefitted me well to do without the association with the English alphabet.