I would also recommend Celia Hammond. They have a busy cattery at Lewisham.
Extract from website as follows:
Volunteering
Help is always greatly needed in a variety of ways such as transport, the collection/delivery of items, home visits and of course, most importantly, fundraising. If you are interested and feel you may have something to offer, even if it is not something mentioned here, we would love to hear from you.
]WE NEED dedicated people to help us with the rescue work (this is done mainly late at night)Trapping feral cats for neutering and/or rehoming using our own specialised equipment and methods, is very time consuming, but so rewarding, knowing you are greatly improving, and, often saving their lives.
We are also very keen to hear from people wiling to help with the day to day cleaning and feeding of the animals. Do you live anywhere near our branches? Would you be prepared to muck in?
If you can help as a volunteer, you are dedicated to animal welfare, and want to make a real difference helping animals in the face of this challenge, do not hesitate to contact us info@celiahammond.org