Yes, in England, VED is hypothecated to the National Roads Fund, almost all of which is spent on the Highways England road network. Not sure how the non-English part is divided up.
This is a particular sore spot in London, because TfL doesn't receive any VED money, doesn't receive a local maintenance grant that local authorities, and no longer received a general subsidy grant from central government. So TfL's road network is paid for entirely by council tax payers and whatever other income sources TfL has.
(some people like to describe this is tube passengers are subsidising car users, but the tube doesn't make a net profit once you account for capital spending, so that doesn't quite work)