All cars were in demand in WWii and for several years afterwards, for the very simple reason that new cars weren't being made in any quantity, and those that were were not for UK public purchase!
In fact, many pre-war cars stayed on the road until 1960, which saw the introduction of the 10-year motor vehicle test, which was a boon for special-builders but saw many cars consigned to the scrap-heap, including some classics with very little problems.