Hi Widget

With the cable slipping ,you can just get a hose clamp and tighten the clamp around the handle bars and the cable
so the outer cable is now fixed to the handle bars ,I would lubricate the inside of cable first.

The spring fits as in pics below ,I would assume.

Fit the spring and see if that's better.

Cheers
Max

Attachments
hose clamp - Google Search.png (31.56 KB, 67 downloads)
Mower Base Supaswift Big Bob Series aa.jpg (26.72 KB, 67 downloads)
Mower Cable Lube.png (15.44 KB, 67 downloads)
Mower Spring.jpg (72.54 KB, 67 downloads)
Mower S Cable a.jpg (86.03 KB, 67 downloads)
spring 1a.jpg (145.59 KB, 63 downloads)