I have been given an runner bean seed which is meant to be over 100 years old. How do I find out the variety of bean?

There's a seed bank somewhere, can't remember where though, might be Kew - you could ask the RHS or contact Kew Gardens.

welcome to GOY Astralady.
the millenium seed bank is at Kew in
the country ie Wakehurst Place near Ardingly. wether they will have the records there is uncertain.
You may be better asking at the RHS for lists from seed catalogues. but unless it is grown you are unlikely ver to find out.

I am curious, Astralady. Is your seed itself 100 years old or is it a seed from a variety that is 100 years old?
Either way, I would think that the seed bank at Kew, as suggested by Sbg, would be your best option.

Thank you all for your help. The variety is over a 100 years old - not the actual seed - sorry for the confusion. I will send a seed to Kew from ones I have grown this year. Thanks again and happy gardening.