UPDATED February 2012
The Raleigh Twenty has a proprietary 76mm wide 26 threads per inch bottom bracket, unique to this bicycle. You are somewhat limited in your options, but below are outlined the main possible courses of action:
1.) Get a new Bottom Bracket and 26tpi rings from Phil Wood & Co.:
The easiest, but most expensive option.
2.) Find a suitable cotterless spindle
and retain original bottom bracket cups:
Easiest and cheapest replacement for the cottered spingle. Kurt from The Headbadge had a small supply of these which are now out of stock. He's looking around for more. If he finds any we'll advertise it here, but since it is an old stock item, it is hard to find. So far reports have been that it is a perfect retro-fit, but it may depends on the particular crankset you intend to use.
3.) Modify the Bottom Bracket Shell to take a threadless bottom bracket:
Here is a photo set from flickr showing how someone used a threadless cartidge bottom bracket in 73mm wide frame. For the Raleigh Twenty, you will need to remove 4mm from each side of the bottom-bracket shell. (The Raleigh Twenty has an unusually-wide 76mm shell). If you mark it out properly and work carefully you can probably use a hack-saw to remove the unwanted sections of the bottom bracket shell. Be careful, and leave plenty of room to use a file to dress the shell down to size. The best way to get it down to precise width is to use a bottom-bracket facing tool.
4.) Have the bottom bracket narrowed to 68mm and re-threaded to 24tpi.
One of our site members, Luke, had this work done by Alex Meade Bikeworks, showing us a full example of how a bottom bracket shell is modified. Click here to see all the gallery images and his comments. Here is a brief summary showing what he has done:
The bottom bracket shell has been narrowed with a milling machine and now new threads are being cut into the bottom bracket shell. The new threads will go much deeper than the original 26tpi ones, so plenty of cutting lubricant is needed and the threads are quite strong. The taps being used are professional tools found in bicycle frame-builders shops. Probably too expensive to be worth buying for a home builder, and unlikely to be loaned out by a bicycle shop.
Whilst a milling machine has been used to remove most of the excess width of the bottom bracket, a bottom bracket facing tool is used to remove small amounts of metal until you get down to exactly 68mm. Again, not a cheap tool for DIY people. If you can get your hands on one for this purpose, consider yourself very lucky! The tools for this work will be held by a frame builder, so consult them to see if they are willing to do the work for you. Chances are it will be much cheaper than buying the tools!
Here is the complete bottom bracket with a newly-fitted Shimano UN52 catridge. PERFECT FIT! He makes it look so easy doesn't he? I've emailed him about advertising this service here - will get back to you on the price of this work.
Luke informs me that this whole job was done by Alex Meade Bicycle works for $85 US.