I believe, and correct me if I'm wrong, that Nationwide still use roll numbers for certain accounts, as opposed to sort code / account number.
Is the account number a memorable number, e.g. 11111111, and you supplied the roll number as the payment reference? If this is the case, there is likely a degree of manual intervention as the payment will not be routed via Straight Through Processing.
Your bank cannot possibly confirm that the funds are in the account, it's just not possible. At no point can they look into an account held at another bank, so this part is incorrect. They can confirm that the funds have been sent to that sort code, but it's up to Nationwide to apply it to an account. If they are unable to apply the funds, they will be bounced back to your bank and may be sitting in a rejections account somewhere. Your bank needs to open an investigation where Nationwide can then look into it there to confirm the location of the funds.
Don't go down the small claims route yet until you have irrefutable proof from both banks as to the location of the funds.