In World War II, the Yorkshire-born entertainer, Wilfred Pickles, was asked to read the national radio news because the authorities felt his dialect/accent would be far harder for the enemy to copy and sow seeds of doubt among the listeners.
Almost immediately, his use of the short ‘a' - typical of northern dialects - as in bath compared with baarth, was criticised and a torrent of further abuse appeared in correspondence about using him. A newspaper headline actually appeared reading, "Lahst a Thing of the Pahst"! Poor Wilfred was rapidly removed.
English dialects have always shown differences in vocabulary, grammar and structure as well as pronunciation. People who spoke in what used to be called Received Pronunciation (RP) were basically just using the 'dialect' of the southern, educated classes...public school, Oxbridge, government, judiciary, society etc. (I use the word, dialect, in the sense described in Chambers...ie a language peculiar to a district or class.)
Even today, a barrister in Canterbury might say glaarss and baarth with a long vowel, whilst a Preston butcher might say these words with a short vowel, each fitting into his particular district and class limitations.
The reason is almost certainly because of the phenomenon known as the Great Vowel Shift. This affected the pronunciation of the language in southern England between the 15th and 18th centuries, basically involving the long vowels transforming into diphthongs. For example, the Old English word for house was hus with an ‘oo' sound, but by the 1500s that had become house with an ‘ow' sound. Such changes did not, of course, take effect immediately everywhere, but at different rates over the centuries, depending upon regional and social variations. In addition, some of them did not happen at all in certain areas. A house, for example, is still called a hoose in Scotland!
The same is doubtless true of the short northern ‘a' in b