Not that old... It stopped paying for roads specifically in 1937.
"A vehicle tax was first introduced in Britain in 1888.
In 1920, an excise duty was introduced that was specifically applied to motor vehicles; initially it was
hypothecated (ring-fenced or earmarked) for road construction and paid directly into a special
Road Fund. After 1937, this reservation of vehicle revenue for roads was ended, and instead the revenue was paid into the
Consolidated Fund – the general pot of money held by government. Since then, maintenance of the UK road network has been funded out of general taxation, of which VED is a part.
[4]"