I may be out of my depth but...

[hobbitonabike]

What is the best way to deal with these wheels? Is there anyway I can get them looking shiny again or are they a lost cause?

 

[winjim]

Try Autosol metal polish.

 

[Apollonius]

Almost impossible to re-chrome steel wheels successfully. Try to pick uo a pair of alloy rimmed wheels on ebay or similar. Yours might be 27" or they might be 700c. Only about 6mm difference, so both should fit.
Attacking them with a Brillo pad might produce something usable, but they look a bit far gone to me.

 

[roadrash]

if you want to try and clean them up, which i suspect you do ,rather than replace them ,have a look on youtube , foil and coke rust trick, . may be worth a try

 

[JasonHolder]

Get new cables. Inners at least.

Old ones get wrecked trying to feed back into outers have fun! Its a good crack.

 

[hobbitonabike]

Cheers guys. Would like to have a crack at making the most of what is already there if I can. Obviously I will need to replace some things but wherever possible I am going to try and restore rather than replace.