Save the paint!

Did you attempt this yet? I would:

• clean the frame
  
• remove any rust with lemon juice and wire wool
  
• wash again
  
• polish paint with T Cut (my go-to method) or there are more gentle polishes... Autoglym Paint Renovator
  
• wipe down with damp cloth
  
• pre-wax cleaning/prepping compound, it's like a milky fluid, then buff that off with a cloth
  
• finally a wax like RaceGlaze, two coats, you can get tiny tubs for around £5-6
  
  

Example of this process:
https://www.lfgss.com/conversations/351054/