Andy, I've just been looking to see if English Heritage have any properties near Leicester, but the nearest one (which would probably have work for volunteers) seems to be Kirby Hall, about 20 miles away. National Trust have Stoneywell and Calke Abbey. Have you any museums or art galleries where you could help out? My only other suggestion is to search in your local library for any vacancies.
Best of luck in finding something which suits you.