Myself and my partner have recently adopted a 12mth old English Cocker Spaniel from a NW rescue organisation - and he has settled in wonderfully in many aspects and is showing great confidence now. 

We have some patchy information received from the previous owners describing why they had to hand him over to the rescue org' which includes a dislike of other dogs.

We have tried to gently introduce another family members dog (a Shiht-Tzu). But at a distance of  10m or greater our cocker spaniel acts very intrigued and excited and may bark.

When they are in close quarters - he is very scared and jumps/hides behind our legs and is frantically barking. 

What is the best method to build his confidence so he can interact with other dogs happily?

could you try just going on walk with the other dog and family member? see how he does then just gently getting used to him being there, but also having an enjoyable walk.

Yep. Keep him as exposed to as many other dogs as possible but within his comfort zone so you can easilt keep his attention on things he likes and so that you can stay relaxed and keep the lead loose to reduce the tension. Get him to focus on doing actions for you, playing with you, and not focusing on other dogs.  I like to get them to look at the other dog and before they can react junp in with a good boy and turning around a copule of times to disrientate them and the turning round with you practically stops them being able to hide or look at the other dog and then step away reward and do some distraction training and then moocve again closer to the other dog and repeat.

Most likely the previous owners couldn't be bothered to socialise him and once they created his problems they couldn't be bothered to work through them.

A couple of months back we had a new to a family rescue Patterdale terrier from Hell arriving at dog class. Totally unsocialised and couldn't even look at another dog at a distance without getting frantic. The owners had had dogs all their lives but never one with this type ( or any type of ) aggression!  They listened to our advice and worked hard with this dog and this week they have a new problem! How to stop him wanting to play with other dogs!  Well I tople them not to just yey and give him longer with the diastraction training, and confidence building  and he should then gradually get more focused on them anyway.

If you need more help it might be a good idea to find a trtainer who can demonstrate what to do to keep him upbeat without teaching him to avoid other dogs because it is a bit difficult to describe.