There was some discussion on John Wells’ blog a couple of months ago (here) about traditionally SBE BATH words now being increasingly reported with TRAP. John said “The fact that more younger people than older report a preference for /ɒ/ in one and for /æ/ in chance can be seen as a greater willingness on the part of northern respondents to report a preference for their own pronunciation in cases where it is known to deviate from the perceived norm (RP: wʌn, tʃɑːns).”
I should like to propose an additional explanation. As John himself says in AoE: “The TRAP-BATH Split … represents the ossification of a half-completed sound change, which seems to have come to a stop well before completing its lexical diffusion through the vocabulary which met the structural description of the lengthening rule.” (page 233) This has led to the formation of the group of words that John classifies as 59ʹ (to which I would add aftermath, and Belfast among fairly common words. I should also move Iraq, Iran and Sudan into this group from 59c. I realise none of the groups is supposed to be an exhaustive list). This group of words can easily lead to confusion in the minds of SBE speakers. I suspect that no consonant cluster invariably triggers the Split – exceptions can be found in almost every case:
staff but gaff(e), path but maths, brass but lass, after but caftan, grasp but asp, master but aster, ask but Gascony. And so on.
I have heard TRAP pronunciations in many supposedly BATH words from speakers of otherwise clearly southern varieties of British English, who were born and brought up in the southern part of England. They were sporadic – i.e. of particular words and not throughout the class. Could it not be the case that the sound change may be reversing itself to some extent, presumably because it never was completed, and perhaps because of the influence of American English, where many of these words still have /æ/, but also from the influence of the increasing numbers of Northerners who are heard speaking with confidence in their own accent, which may be raising the uncertainty levels of Southerners in specific cases? Increased geographical mobility has also led to large numbers of Northerners living in the south, and having children whose accents are affected by both influences: words learned at home with TRAP but those learned in the street or at school with BATH (grass and bath, for instance, are likely to be learned at home from parents, but master, staff from a wider acquaintanceship).
Another quotation from AoE: “There are many educated northerners who would not be caught dead doing something so vulgar as to pronounce STRUT words with [ʊ], but who would feel it to be a denial of their identity as northerners to say BATH words with anything other than short [a].” (page 354) As I first read this, I nodded to myself – I have only a handful of words with /ɑː/ whose spelling is not either ‘al’ or ‘ar’, and these include words with final -a such as spa and bra, which could scarcely be pronounced in any other way than with /ɑː/.