Removing Rust on Chrome Rims
If you want to keep the steel wheels, you need to remove the rust and stop it coming back.

For Pinheads of Rust


Strip off everything that is not metal (tyre/tube/rim tape)
Poke at the big rust spots, look for rust under the chrome.  You need to expose the rust to treat it
Sand off any large lumps of rust with sandpaper (this is tedious)
Treat the whole wheel surface with a rust resolver like "Rustbuster" which is an acid.  Use gloves and eye protection - this stuff dissolves skin nicely.
Allow it to dry/cure overnight
Next day, sand any lumps of black rust ready for painting
Immediately prime the whole wheel, spraypaint works well.  Then immediately wipe the primer off the chromed parts because it won't stick there anyway.
You can try applying a spray chrome paint last.  Avoid the brake track, it won't last there.


Personally I used grey primer and simply left it at that.

Significant Rust

If the rim is too rusted then you're up for some more in-depth work.  If flakes of chrome come off because of rust underneath, then its significant.  The rust will have penetrated under the chrome, and its very hard to get to.  So the fix is to take it all off.


Disassemble the whole wheel, loosen all the spoke nipples, remove the bare rim hoop.  Order replacement stainless steel spokes and brass nipples.
Send the rim hoop to a commercial shotblaster for cleanup, with whatever product they recommend.  Could be glass pellets, walnut shells, sand, or similar abrasive powders.  
While these steps are happening, service the hub with new bearings etc.
Once the whole rim is bare metal, get it commercially rechromed.  A proper chrome expert will know the appropriate grades to use so the brake track works.
Reassemble with new spokes and nipples (you may as well do it right) on the fresh hub.




Upgrade for Safety

Personally?  I'd scrap the steel wheel, and replace the whole rim with a modern alloy rim.  This will make braking work much better too.

Downside, is that modern 700c wheels are a few millimetres smaller than your existing 27" wheels.  So the brakes have to reach a bit further, and you need new tyres.  Your spare tubes should be okay though.