Smart women and men in dark suits for business lunches strolled past the mirrors and pink sofas in the hotel lounge. Mr Marx, with lady secretary following, came across, travelling fast like a shark through the shoals of porters and pageboys – a small athletic figure with pale-blue suit, white tie, cigar between teeth and on his head a large white cap of the sort Gene Sarazen used to wear for golf. We greeted him and together made for the door. As we approached it, he put a hand out to slow us down for a moment: "Cricket, eh?" he said flatly and then headed towards a taxi.

Our attempts at ordinary conversation seemed unnecessary as Mr Marx sat there looking wary and sardonic, smoking away at his cigar. We said we hoped he wouldn't be bored coming to Lord's with us, that it was just the MCC playing Cambridge University – like Yale and the Dodgers – and that Cambridge would be fielding.

"Fielding?" said Mr Marx abstractedly. "Didn't he write Tom Brown's School Days?" Well, no, he wrote Tom Jones. "Tom Jones's School Days?" said Mr Marx looking out at the Edgware Road.

The taxi drew up at the Grace gates.Mr Marx was first out. He offered to pay for the taxi, holding out a neat brown hand with two florins in it: with this gesture, somehow, everyone relaxed. We bought his and Miss Hartford's tickets. "Come on, let's go," he commanded. We stepped forward into the ground as he wheeled round, cigar held in front of him, travelling through the gates. He accompanied us round the back of the stands, looking marvellously incongruous in his white cap. Could there be a game on? he asked; a baseball game in New York could be heard blocks away. He glanced sideways as we passed at the notice on Q stand which says "Members and friends", remarking: "That's the most ambiguous thing I've ever heard."

We rounded the back of the pavilion and there it was. The ground was practically empty: a hundred people outside the Tavern, a few in the stands, 20 or 30 members in front of the pavilion. The players, one of them an Indian in a pink turban, in two motionless groups waiting for a new batsman. The scoreboard said 74 for 5. The place was quite silent. It looked like rain.

We sat down in the front seat of A stand: we were alone there. Mr Marx's eyes went round: "Is it always as crowded as this? Does it get enough money to pay for the ball?" He continued observing the scene. "What a wonderful cure for insomnia. If you can't sleep here, you really need an analyst. Doesn't that maharajah with the whiskers get tired pitching? Even the men in the tradesmen's coats are trying not to watch it. Umpires, eh?"

He noticed the small crowd in front of the Tavern, asked if that was where they put the dead bodies. We explained there was a bar there open all day. How long did the game go on? From 11.30 to 6.30. "Boy, by six-thoity they must be really loaded," he reflected.

We began to talk seriously about sports: he asked whether we had ever attended a ball game and hearing that we once had, questioned us closely to establish exactly which one it had been. He was sure cricket was a good game once you learned about it. He discussed tennis, said his son ranked 12th in the United States. Mentioned that he'd seen Budge Patty, who is a friend of his, in Paris.

He questioned us on amateurs and professionals: then asked how English society had changed since the war, from that he mentioned the recent Supreme Court decision about the education of negroes in the United States. We asked whether the southern states would be able to get round it: the drift of times was against them, he thought.

"And children don't think like their fathers," he remarked sagely. His conversation on such subjects was mellow and tolerant, with only the faintest hint of other possibilities.

Would Mr Marx like to visit the pavilion? On the way, a spectator leaned over with his scorecard. "It is Mr Groucho Marx, isn't it?" Groucho signed with a sudden accusation: "Were you the guy making all the noise back there?"

As we approached the door of the pavilion, we explained that this really was the altar of English cricket, a venerable palace. "Don't worry," he said, "I've met stuffed shoits before." In the Long Room with its air of linoleum and dignity, Groucho sniffed and looked around.

"Where's Haabs?" he asked. "That's the only name I know in this business." We showed him the large painting of WG and other portraits. Suddenly he leaned forward: "I never knew girls played cricket." We asked what he meant. He gestured his cigar at an 18th-century painting of a boy with fair hair standing among trees and leaning on one of those curved bats.

Groucho inspected it closer. Under the painting was written: "Youth with cricket bat. c1790." "Youth, huh? 1790, eh? I guess this business started earlier than we thought."

From time to time Mr Marx glanced out through the closed windows at the game. "How long can they be without running?" We said it could be a matter of days theoretically. "Is that so? And at night, they play with phosphorescent balls?" He shook his head in wonder.

Mr Marx was then introduced to a high official of the MCC, accustomed to dealing with visiting celebrities. "You're over here on holiday, are you, Mr Marx?" Groucho stroked his chin: "I was until I saw this game."

As we left, the doorman suggested we show Mr Marx the museum. Groucho's eyebrows went up. The doorman reminisced enigmatically: "We had Mr Rockefeller here, too – he used a lot of baseball terms." "Aha," said Groucho, "but he was richer than I am."

Out in the street he bent down to make a funny noise to a child in a pushchair. He looked happy, but he had never actually smiled the whole afternoon.

The next day he called to say goodbye. There he was with Miss Hartford, standing outside the hotel waiting for a car to take him to the airport. He had on a neat brown trilby and no one recognised him.

He and Miss Hartford climbed into a large car. They had not much time to get to London airport. As they were leaving, Groucho flung open the door. "Can I drop you any place?" We said no, we were going in the other direction. "Cable me the result of that game," he called.

This is an edited extract