How to adopt an adult dog

Following the sad death of one of my beloved dogs I am now ready to give a small adult dog a loving home. My remaining dog is 13 years old and missing her companion too.
The local cat and dog shelter has mainly Staffy and Bully types which are not what I am looking for.
Ideally he/she would be about 5 years old and small enough for me to lift into the car.
I have registered with the nearest Dogs Trust but don't know where else to look. There are LOADS of puppies advertised for sale on the internet no doubt hoping to cash in on Christmas, it's frightening.
I'm not looking for any specific breed and don't want to travel too far, I am in North East England.