I've not had a lot of emails for this site recently and I am very busy with my course, so I've decided to stop updating it - your best bet for degu rescue is probably Pet Rescue Forums
Please note that inclusion on this page does not mean approval by this site. It is particularly important when you are rehoming your pets to make sure that they are going to a good home - I cannot check the people that I put on so it's up to you. One of the most distressing things is that every year there are cruelty cases involving self-proclaimed animal rescue centres who just took on more animals than they could cope with.
Places to look for a degu, or a home for one.
First of all it is worth calling around the RSPCA centres in your area as they occasionally will get degus in, or know of another centre that has them in.
Pet Rescue Forums - has a Rodent - Homes Needed section that often features degus. The also have a rescue centre list.
UK Animal Rescuers - has a comprehensive list of rescue centres. Rescue centres generally know each other so may be able to put you on to someone if they don't have any degus currently. Also often they can help with transport.
More small animal rescues at Cavy Rescue. Email and ask - there's often degus looking for homes.
The adoptables page on Cavy Rescue has a search engine where you can search for degus needing a home.
The Degu Information email group has quite a few members who may be able to help. There is also a breeders/sellers database (you will need to register to access it).
Animal Rescuers has a page with details of rescues that take rodents and rabbits.
Whilst mostly concerned with chinchillas Chinchillas Un limited discussion forums has a rescue area for other pets that sometimes features degus. This is also well worth a post if you are looking for degus as a lot of the chinchilla rescue people that are members get in degus or know someone who has degus in. Mention that you have come via here so I don't just direct you back :)
The Degu Guide site has a degus wanted/for sale page that is updated regularly. Most of the degus are in the US but there are some UK listings.
Bella UK has a list of charities and also a small animals requiring homes page.
Cavy Rescue classified ads often have degus.
Guinea Pig Rehome has lists of guinea pig rehoming centres by area. These often end up with degus and so are worth contacting if you are looking for a degu. If you are looking for a home for one then chinchilla rescues are probably a better bet.