They not only had my frame in stock, but immediately offered to replace the entire frame for the cost of a replacement part ("it's our policy"). So I paid £35 for a brand-new frame priced at £125.
I was told they would have the lenses swapped over in about half an hour, and I handed over my glasses. The staff looked at my lenses, had a brief confab, and informed me that because I was so short-sighted the lab technician was going to do my glasses straight away, rather than make me blunder around the streets or stare blankly at a wall until they were ready. Thus it was mere minutes later that a new, working frame was placed on my nose and carefully adjusted.
Very, very pleased with this outcome. I moved to Specsavers after a couple of annoying and disappointing experiences in different branches of D&A, and I cannot recommend them highly enough.