British upper-class pronunciation of words like "what" and "when"

Solution 1:

Only a few dialects maintain the distinction between /hw/ and /w/, that is, distinguishing witch from which, wale from whale, and wine from whine. The WH sound, a voiceless labiovelar approximant, is written as /hw/ or sometimes /ʍ/ in the International Phonetic Alphabet. The W sound is a voiced labiovelar approximant. The difference between the two is that the WH sound is voiceless, meaning it is produced without vibration of the vocal cords (at least at the beginning), whereas the W sound is produced with voicing (vibration of the vocal cords) throughout.

Wikipedia has a good article summarizing the phonological history of the WH sound.