Causes for output transformer failure?

[Sideband]

C21 is a disc ceramic so is likely to be in good condition. Looks like you've made a good job of changing the old waxy caps. Most likely the reason for the demise of the transformer is as previously suggested....Corrosive gasses (very very small amounts indeed) given off by the batteries in the confined space of the cabinet, combined with damp (read seaside) use. It's also possible that the transformer failed while in storage. Damp just got into the winding over the years and eventually ate through the very thin primary wire.

[G6Tanuki]

"Green Spot" corrosion is traditionally the way transformers wound with very-fine enamelled-wire die. Doesn't just affect output-transformers - the IF transformers in many radios stored in less-than-ideal situations also suffer from it.

A pinhole in the enamel, a damp/corrosive environment, aided by 100 or so Volts to provide a weak electrical-charge to draw-in floating particles....

Another cause of output-transformer failure can be working-without-a-load: particularly a problem in radios that had switching to connect an external speaker. If it was switched to 'extension-speaker' but no speaker was connected, the voltages across the primary-winding of the transformer could get a bit wild and punch-through the insulation.

If it didn't immediately fail, the scene was nevertheless set...

[Herald1360]

A small 6VA mains transformer with 4.5V secondary windings will probably fit and will give you usable sound. New would still cost about £10 though.

If you fancy having a go, any 6VA mains tranny with a split bobbin winding could be dismantled and the secondary rewound for about 4V- note the original voltage, count the turns as you unwind to get the turns per volt figure then rewind the number of turns needed for 4V.

All good fun