You can find some of the more generic parts on eBay, however there are a couple of decent stores of used/spare parts online.
Leacy Classics – This company has recently acquired all of the stock from London Taxi Exports. They are in the process of moving it all up to Birmingham so it can all be cataloged. Their website will be updated with listings of the parts, however in the meantime (as there is so much stuff) it is best to ring them up and see if they have it. Once all the stock is on their website, it will be an accessible goldmine of Fairway parts! Call Phil and he is a font of knowledge and will help you out.
You will also find plenty of people online who ‘break’ old Fairways for parts. You can find details of regular breakers on the forums, which I’ve listed here. If you’re may be looking for some inspiration, there are some great websites made by other drivers and restorers here.