A bit more than a year ago, I was musing about this question: What is the number x, such that there are x settlements in the United Kingdom which have a population of at least x? Are there 10,000 towns of 10,000 people? - clearly there are not. Are there 1,000 towns or villages of 1,000? - yes and plenty more. In fact, based on 2011 census figures there are 2,374 towns or villages with at least 2,374 inhabitants.
Of those 2,374 places, there was precisely one with no public transport of any kind. It was Wynyard Village, a gated community about three miles west of Billingham in the Borough of Stockton on Tees. You have to be fairly rich to live in Wynyard Village - Duncan Bannatyne used to own a house there, for instance - so it's perhaps not surprising that its inhabitants have little need of buses. Even so, if you are surprised that this possible answer is in the north east of England, when you might have expected it to be somewhere like Dorset or Herefordshire, well so was I.
Now, it possible that some villages larger than Wynyard (population 2,683, according to the 2016 official estimates) have lost their bus services since I made that discovery and so I cannot claim that it is definitely the answer to your question. But an opening bid, in any case.