What an inspiring, thoughtful and caring post, I am very pleased that things have worked out so well for you, and long may that be the case.
Have you tried contacting the Haven Centre in Fulham
www.thehaven.org.uk, they have provided invaluable support to friends of mine in exactly the same situation. My sister-in-law up in Scotland has been through surgery and is now undergoing chemo and I was trying to find support for her similar to the Haven but sadly there was nothing like it up there. If they can't find another lovely home for your wigs directly they may have some other ideas.
I found a wonderful website when looking for a home for my wedding dress,
http://www.weddingwishingwell.org.uk/ which may also be worth contacting, I have no direct experience of their work however.
If absolutely nothing comes from NVN or the Haven, then the National Theatre has a costume and props hire warehouse in Kennington, and they may be happy to take them too, lots of schools and drama clubs hire things from there at very reasonable rates, it is a great resource.
All the best wishes to you.