I found an old cigarette in my attic and my house is over 100 years old. I searched the brand name on Google and I'm pretty sure it's the cigarettes that they made from 1952-1956 and were banned for having crocidolite abestos in them. Would this one cigarette be worth anything for being almost 60 years old and banned?

Nothing. Original and unopened packs may be worth £50 to £100 to a collector, but the problem would be selling it. I used to see these on eBay a few years ago, but no more. The main problem is that it is illegal to sell asbestos products and then there is also the question of safe carriage. Your main concern should be to ensure that you are not exposed to asbestos fibres from this cigarette and I would keep it double bagged and labelled in a completely airtight container.