HIGHGATE CEMETERY, LONDON—On a summer visit to the grave of Karl Marx, Ben Gliniecki found that he would have to pay £4, or about $6, to pay respects to the man who sounded the death knell for private property.

Mr. Gliniecki, a Marxist, said no.

“Personally, I think it is disgusting,” the 24-year-old political activist said. “There are no depths of irony, or bad taste, to which capitalists won’t sink if they think they can make money out of it.”

The charity that looks after this cemetery has long taken swipe at a different irony: Karl Marx’s decision to buy a burial plot in a private London graveyard over the then state-provided alternatives. They say their cover fee subsidizes the upkeep of a cemetery where 170,000 other people rest.

The two sides have squabbled since the early 1990s, when the Friends of Highgate Cemetery began charging to fund the conservation of a burial ground whose elaborate gothic tombs and winding paths had fallen into disrepair. Now, the charge is infuriating a new generation of Marxists. Interest in his legacy is gaining fresh legs in Britain following September’s election of Jeremy Corbyn, a self-described Marx admirer, as leader of the opposition Labour Party.