Who knows about solid axle sizes?
 

I have acquired a mid 1970's Raleigh Europa 10 speed racer and it has high flange steel Sturmey archer hubs with solid axles.
As a tidy up I'd like to replace the original nuts with integrated washers possibly with wing nuts.
Would they be standard 5/16 front and 3/8 rear or does Raleigh and Sturmey Archer have proprietary sizes?

It's not a proprietary thread, but I'm fairly sure it's a BSC 5/16x26tpi vs. a UNF 24tpi.

The easiest way to know is to bring the axle to a hardware store and test a 24 thread nut to confirm that it doesn't fit. The right nut should be available at any decent bike shop, though I suspect that many newer shops may not have it.

Axle nuts are pretty easy. They're usually numbered like this: first number is length in millimeters. Second number is diameter in mm. Third number describes no. of threads per inch. 24 threads per inch is pretty standard stuff. Most new rear axle bolts are 10mm diameter. You're going to have to get a measuring tool to make sure of what you got. A cheap Chinese caliper is about $10. Borrow one or, you can also just use a plain old ruler. A new rear axle can make a bike run like new. Be good. Have fun.

Having said all that, there's a number of non-standard wingnuts in the marketplace and I've got quite a few of them. Some don't fit anything or any axles that I have.

I've swapped out several axles on the old bikes I buy. I bought an old 80's something Raleigh that looked like it had only been used once. Not a scratch on the bike. Rear axle was bent so bad that the wheel wouldn't even rotate. It was a solid bolt on type. I ordered a replacement that included the cones, spacers, washers, & locknuts. Never considered trying to put wing nuts on it. But, what the heck. Sounds like a cool idea.

I often wonder what happened to bend that axle. Maybe somebody that weighed 350lbs got on the bike and crushed it. Put the bike up & never rode it again. I got to say it cleaned up real nice. The red paint looks practically brand new.

If your dropouts are not parallel, that puts a bending stress on the axle when the nuts are torqued. Consequently, the axle will bend when submitted to loads that are smaller than normally required to bend an axle. The load required to permanently bend the axle is inversely proportional to the misalignment of the dropouts.

I think your right about 26tpi. I took the rear to the lbs and appears to be 3/8 but a different thread. Been able to hunt down a set of raleigh wheel nuts in good nick with an 'R' on the caps same as the original.