Am I entitled to a valuation refund?

OK, so this is a bit of a complicated story.

I went to my bank and asked for a mortgage. They effectively said no problem, credit checks were fine so I paid my money for a valuation. The next day, they tell me that I couldn't have this mortgage so they withdrew their offer and gave me a refund of all the fees I paid. Fair enough. I then realised that they had carried out a valuation at my property anyway but of course, was not billed for it.

A few months passed, and I decided to try my bank again for this mortgage. A new application was made and I was accepted again. I paid my fees and waited to be told about valuation. The bank then tells me valuation was ok - great!

I then got a letter through the post basically stating that they didn't carry out a new valuation and just used the one from a few months ago. I asked for a refund but they refused, saying that I never paid valuation to begin with. My argument is that I was led to believe that the fees will be spent on another valuation and since they were not, it is not up to me to cover their previous erroneous valuation.

Legally, where do I stand? Is it a reasonable request?