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@lae
^ it's not necessarily 26tpi - I had a 1980 Raleigh Magnum and that was standard 24tpi. That said, since this bike has cottered cranks, it's 26tpi in my experience.
It probably isn't a 71mm shell - I think only the Raleigh Twenty used those. My girlfriend's 80s Caprice uses cottered cranks, 26tpi but 68mm shell.
You can get cotterless axles for 71mm shells; they're quite rare. You could face down a 71mm shell to 68mm and use a standard cotterless axle. Or, if you wanted to use a sealed BB, you could use a threadless bottom bracket.
Or, you could just use cottered cranks - they're not so bad once they're installed properly, and since they're usually made from steel they're extremely hard-wearing. Since this is a cheap frame, I would avoid spending unnecessary money on it and just use cottered cranks - the cheapest option.
If you do want to remove the cup, you can try to unscrew it with a big adjustable spanner. Sometimes they come off with a spanner, sometimes you need to use a vice, sometimes you need to use the proper tool (i.e. take it to a shop). Soak it in plusgas first.