the Celts quite likely did speak some Latin, though not necessarily all the time. Like Norman French later, Roman may have been the language of the conquerors but not of their subjects - those not in regular contact with the new rulers would have had no need to speak their tongue.
The Angles and Saxons didn't really destroy Roman civilisation, it just seems to have gradually withered away. For instance, they didn't move into the remains of Roman London but congregated further upriver.
I don't think Christianity was all that strong under the Romans, but the Angles and Saxons, though they were pagans when they landed, were converted maybe 100-200 years after arriving in Britain. They then built the churches and monasteries that were later attacked by Vikings.