An accent in spoken languages is a particular style of pronunciation that gives cues about the speaker's background such as their region of origin, age, schooling and/or social class. For example, the vowel in 'bus' and 'nut' (and many other words with the same vowel) is generally pronounced differently by speakers from Manchester compared to London, even though the words in each part of England are the same.
BSL definitely has strong regional variation, but the variants are better considered to be dialects rather than accents. The reason for this is that the variants are more about what you say (i.e. signs - equivalent to words in spoken languages) rather than how you say it (i.e. pronunciation).
Signs for colours, numbers, countries and place names, among others, show a high amount of variation in BSL. For example, quite different signs are produced in different parts of the UK for the concepts 'green', 'seventeen', 'America' and 'Birmingham' - see BSL SignBank for documentation of many of these regional variants. Historically different variants appear to have developed independently in different deaf schools around the country. However, some of these patterns appear to be changing. Evidence from the BSL Corpus suggests that younger deaf signers all over the country are using fewer traditional regional signs compared to older deaf signers. This is one reason why documentation of BSL (e.g. via BSL SignBank and the BSL Corpus) is so important, so that we can document this regional variation and keep a record of older forms of BSL in the long term.
So far there is very little evidence that the exact equivalent of accent exists in sign languages. One possible equivalent is a 'hearing' or 'late learner' accent. People who learn sign languages as adults consistently produce signs using bigger movements produced by joints closer to the body (e.g. the shoulder and elbow joints) than native signers/early learners who in the same situation might use joints further away from the body (e.g. wrist and finger joints).
Bayley, Robert, Schembri, Adam C, & Lucas, Ceil. (2015). Variation and change in sign languages. In Adam Schembri & Ceil Lucas (Eds.), Sociolinguistics and Deaf Communities. Cambridge: Cambridge University Press.
Johnston, Trevor, & Schembri, Adam. (2007). Australian Sign Language (Auslan): An introduction to sign language linguistics. Cambridge: Cambridge University Press.
Stamp, Rose, Schembri, Adam., Fenlon, Jordan., Rentelis, Ramas., Woll, Bencie., & Cormier, Kearsy. (2014). Lexical Variation and Change in British Sign Language. PLoS ONE, 9(4), e94053. http://doi.org/10.1371/journal.pone.0094053