I didn't own a Triumph Cub, but from reading about them, they were a very-popular UK ride. Alf Hagon, a legend in all-sorts of motorcycle competition., competed on them early in his career, and the Hagon business still sells parts for them.
I once bought a TR25W 250cc Triumph from a co-worker, he bought it new. He used to ride it to work, until one day he had a minor accident. He parked the bike and after sitting in a shed for decades, he decided to re-commission it. I had to un-stick the piston, the engine was frozen. That took my oxy-acetylene torch, a pressure-treated 4x4 block and a BFH to finally-free it. I probably could have just bored it (had it done, I am not a machinist) but I found cylinder liners were available, I did that. The rest of the bike wasn't bad, it actually withstood the long time in dry storage well. He rode it for a bit, and offered it to me for what I charged him for the work. I eventually sold it to some British guys who came-to Florida and bought a 40 ft. container's full of motorcycles to ship-back to England, where they fixed 'em and sold 'em.
MY 360 Yamaha dirt bike, bought new, once kicked-back on me during a near-winter enduro in Muskegon Michigan, it was called the 'Pearl Harbor Enduro' because it was on Dec.7. I was stopped in a powerline right of way which had about a 6" flood of frigid water below a thin layer of ice. You could look down the powerline right of way, and see all the stalled-out bikes littering the path. "I have plenty of power, I'll get right-through this!" I said to myself. I made it about 75 yards down the enduro route before the bike lost momentum and stopped. A guy on a TS250 Suzuki stopped a few feet behind me, and we decided there was no-way we were going to be able to get down that. We took turns getting our bikes out of that frozen water, and that's where trying to kick-start my bike, the kick-back for-which the 360 Yamaha bikes were known-for, ripped clean-off the heel of my engineer's boot. They had a compression release on the left handlebar, you had to de-coke the mechanism mounted on the front of the cylinder or it wouldn't work. Ah, two-strokes! I still have the bike. My friend with-whom I would attend enduros and hare scrambles, placed that day. He raced a Yamaha 360 MX or a Rickman 125cc, depending on if it was a tight, 'woods' course, or a more-open course where the 360 MX could make good time, it would do an honest 91 mph, fast for an early 1970's off-road bike.