PIP result and backpay

I hope I'm doing this right as just finding my feet in the forum.
I am on DLA lower rate which was have run out in about April 2014. In January 2014 I was invited to complete an application for PIP. DWP wrote to me and said that as they had not yet made a decision on my PIP application they would extend my DLA payments til October 2014. However by that time I had still not had an assessment date and with no notification whatsoever, the DWP continued to pay the lower rate DLA into my account. Due to my health condition I had forgotten all about my PIP claim until I got a letter from Capita regarding my assessment, which took place in May. The assessor stated they must have lost my application form as she had no form and no supporting evidence.

I feel as though I have been cheated by the DWP because surely I should be backpaid to April 2014 when my PIP{ claim began, but by leaving me on extended lower rate DLA through no choice of my own, I believe the DWP do not now have to backpay as you cannot have DLA and PIP running together. Is this right? I had expected that they would backpay the difference between the PIP and DLA rate.

Sorry if my question is longwinded, and thank you in advance

Hi Gordon sorry for late reply as I couldn't find my own post on here, doh! Thank you for your response. It seems unfair doesn't it but there we go. I wouldn't mind so much but it took them 14 months to arrange the assessment but to be fair I was pleasantly surprised as the assessor (from Capita) gave a very honest report.