I make balance transfers all the time, from higher rate cards (at the end of special offer rates) to ones offering new lower rates. Have you already got the Barclays card or were you looking to open a new card to take advantage of the new rate? - if so that might be the problem. A couple of my cards with a high credit limit (not being used) have slashed my available limit - and I must admit I am pleased, I think it's responsible of them not to give me too much risk exposure. The card companies are being very careful at the moment. I suggest that if you still want to do it, don't apply on-line, ring them up and explain your position. That way you can ask their advice before you make the second application - they can do the credit check before you apply, and let you have an idea of how an application would be received.
Btw has the "decline" affected your credit record? I only ask because I applied for a Goldfish card some years back and was declined for similar reasons to you, but it didn't go down as a black mark on my Experian credit check.