The s/arm spindle in my '56 frame won't come out either. It wouldn't when I used it to build up a bike 40-odd years ago. As I needed transport quick and there wasn't any real play when the nuts were done up properly I used it as it was. It's not been touched since (20k+ miles and lots of regular use further on) and the s/arm is still fine.
Replacing those bushes is not a job I'm looking forward to doing 'cos it's an absolute pig of a job. The spindle will be seized in the steel inner of a pair of metalastic bushes, any force applied to the spindle gets absorbed by the rubber. I think the method I've seen most often used is to carefully cut through the spindle ends, inside the frame adjacent to the s/arm, to get the s/arm out. Then burn out the rubber to extract the remains of the spindle, and carefully cut through the steel outer shells to get them out. (Not forgetting to get the spacer off the remains of the spindle.)
Some folks might be able to machine some of the components away if they've got the kit, but it's still a swine of a job, if you absolutely have to do it.
'55 Huntmaster, '56 VH, ' 51 VH, '80 R100RT, '00 Sprint ST (but all those Ariel parts can only make one running bike...)