Although other answers have mentioned the trap/bath split, I don't think that is actually the explanation for the phenomenon discussed in the original post. The word valuable has the trap vowel and not the bath vowel.
The trap vowel is traditionally transcribed as /ӕ/, using the IPA symbol that is defined in phonetic terms as a vowel [ӕ] that is front of center and intermediate in height between open [a] and open-mid [ɛ].
The phonetic realization of the English phoneme /ӕ/ is supposed to have been accurately represented by the IPA phone [ӕ] in an old-fashioned "RP" British accent. However, in many current varieties of English, the trap vowel is often more open. To speakers of these varieties, the RP value of [ӕ] may in fact sound like the "dress" vowel /ɛ/. Because of this, it has been argued that [a] would be a more appropriate phonetic transcription than [ӕ] for the modern trap vowel, and some linguists (such as Clive Upton) correspondingly transcribe the phoneme as /a/ rather than /ӕ/ in the context of British English. (See "The British English vowel system", by Geoff Lindsey (2012) and "The General British "ash" vowel", by Jack Windsor Lewis, for more details about this.)
Although you say "both British and American /ӕ/ are made at the front", the sources that I have read suggest that central or central-ish realizations of the trap vowel do exist and are supposed to be more common in British English than in American English; this may be why your friends mishear the vowel as /ɑ/ when they listen to the British English pronunciation of words like valuable.