Interesting find. My guess is that it’s a 1659 farthing token, privately issued for a merchant. Stylistically, it has some uncanny similarities to this one:
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That example has a letter ‘E’ for Philip Eldred of Wallingford. He was an apothecary and the token says that on the other side, together with his name and family coat of arms. Yours isn’t a match and I’m pretty sure it has a letter ‘B’ rather than an ‘E’ but it looks like the work of the same die engraver. Token manufacturers often used the same essential design for multiple customers, changing only the name, address or business details. Note also that Wallingford is pretty close to the Buckinghamshire border.
Some more intensive searching might turn up a token match for another merchant with a surname beginning with ‘B’.