I used The Boot RepairCompany at Rochkord in Essex. You can find them on-line. They made a fantastic job of resoling an old pair of Henri Lloyd boots which had suffered similar problems to your Dubarrys. Interestingly they used Dubarry soles for the repair. The new soles have excellent non-slip properties too. The repair wasn't cheap but its quality is so good that the fifteen year old boots now look almost new. No connection with the company, just a very satisfied customer.
Tay's a pity. They repaired my old-style pair for €65 about 5-6 years ago. The boots failed in the same manner as yours seem to have, the foam-type material between the soles and the uppers turning into crumbly dust.
One thing I used is urethane glue (ex Aquasure), it is incredibly sticky it is used to glue or mend components which must remain flexible and be watertight, for example holes in fishermen rubber tall boots, or neoprene wetsuits. I used it over the internal stitching in my goretex trouser as they were not waterproof any more and got a couple more season from them. I tried on my leather boots (not Dubarry) and it sort of worked, but I applied it after having tried first contact glue then sikaflex, so maybe I was asking too much; I would use that before anything else.
