Off the top of my head - his argument is a counter argument against the linguistic tradition that the Germanic invaders committed genocide, both literally and figuratively against the native Celtic populations during that invasion and so the native language had no affect on the incoming German.
Archeological evidence says it didn't happen that way at all - there was no genocide. It's not smart to kill all your new slaves and the Old Germans weren't stupid. It IS smart to breed with them and tax the hell out of them.
Which means linguistically, there were a lot of adult Celt (Brythonic)speakers learning Old West German vocabulary to communicate with the guys with big swords, but not the grammar since that's a lot harder for an adult to pick up. And THAT's the language that became English - a proper bastard of Old West German and Bythonic, which, unlike most other pidgins, was allowed to evolve in relative isolation with occasional influxes of invading people with big swords and their languages.
His arguments are a lot more complex that the above. And the Celtic influence theorists are still a small minority. But it does explain so many of English's vagaries.
