Removing vintage pedals

[Smokin Joe]

Drill the cotter pins out, they're only mild steel. You'd need a new chainset as your crank and chainring are one piece. It's a good opportunity to upgrade to a double as they can be cheap enough and a set of shifters don't cost much, whether you'll need a band set on depends what your is now, being an old frame I suspect it would be.

 

[sidevalve]

If it has mushroomed out cut the threaded end off level with the crank. Support the crank on something SOLID [no not a stick -somthing hard] make 100% sure it is NOT under the other end of the cotter pin. Find a piece of rod [steel] that is close to the diameter of the threaded end of the pin [a little smaller is ok] and get someone to hold the bike still. Use a heavy hammer, not some tiny tack hammer and two to three hard blows should free it. If the crankset is steel and you are carefull you could try heat but as I said be carefull with this one.

 

[Dogtrousers]

Arrrr you aren't wrong I'm ready to cry and throw the bike in the nearest skip - not only has the bottom of the cotterpin mushroomed out but it has bent over at an angle and just doesn't seem to be moving. There weren't any nuts on it to start with so I'm assuming the previous owner gave up halfway through the job.

I've watched several youtube videos but I've tried everything. Any more thoughts?

Sheldon's last two suggestions were drilling it out or heating the crank with a blowtorch. I've not tried them but they are both in the angle-grinder league of drastic-ness.

 

[Gravity Aided]

Angle grinder, replace with BB and crankset from 21st century, save yourself a great deal of trouble.
This looks nice ...
http://www.nashbar.com/bikes/Product_10053_10052_502049_-1___204713