I and two friends completed this feat in 1969. This was soon after the first stage of the Victoria Line had opened between Walthamstow and Victoria. I believe there were then 277 stations, though the Wiki article shows 276.
It took us about three months to plan our route. This included a number of “site visits” to interchanges where time was thought to be tight so that we could establish the optimum place to be on the train. We started at Amersham and finished at Upminster and I believe it took us a little under nineteen hours. The father of one of my friends met us at Upminster at about 1am as I recall.
We had, of course, attempted to beat the then existing record (which I think was a bit under eighteen hours). However, we had a major setback at Ongar. We had planned to return to Epping on the same train that took us to the then farthest outpost of the Central Line, but it broke down and could not return. We had to catch a bus and this cost us the best part of an hour, so our record attempt was in ruins.
We had always planned to repeat our attempt but somehow our enthusiasm waned as the years went by!