This thread appears to have conflated two related but separate issues. One is finding an airman's (in this case) service number and the other is obtaining a post 1920 service record.
While there may be the odd case like Imber's of more than one attempt, even with lots of details, to obtain a record, the lack of a service number should not inhibit one from applying with the details you have.
The National Archives files referred to do indeed provide some information but, as Ruskie has observed, detail is scant and a common name will provide a myriad of possibilities.
Searching the relevant document AIR/78/132 for William Redford, throws up, with their service numbers:
WK Redford
WC ...
William.....
William James...(2 of them)
William Albert Hector.
William Edmund...
Redduck26 - do you think you can be sure which is your man? If not, I would suggest you go ahead and apply for his records anyway as Ruskie has already advised. Quoting the wrong number that the disclosures people will then not be able to match to the date of birth leaves you no better off. Whether you could quote them all as possibilities - don't know.
Alternatively, perhaps Mark G will come back to the thread with the number now you have posted the name and date of birth you will have the success that Ellen reports?
maxD