No, Christianity hadn't died out before the Gregorian mission.

Christianity was brought to the British Isles by the Roman Empire, however in the early 5th century the Romans withdrew. That had the affect of isolating Christianity in Britain from the Christian world centred on Rome and Constantinople (Istanbul). This isolation caused a divergence and a uniquely British Christianity began to develop, we call this Celtic Christianity and/or insular Christianity. At the same time, Germanic pagans were mass migrating and settling in the south and northeast of Britain.

The reasons for the Gregorian missions were mainly to correct the perceived heterodoxy of the Celtic Christians, to reconnect them with the rest of the Christian world and to Christianise the pagan Jutes, Angles and Saxons who had settled in large numbers in Great Britain.