"the Roman influence of England, in the grand scheme of history, was minimum"
Well, except for that Christianity thing.
Roman Christianity, as established by the Empire disappeared for over a hundred years. However, in the celtic lands, Christianity still flourished but with out connection to Rome. It was Pope Gregory who sent out Augustine to ensure that England became a Roman-church strong hold, and to push out all Celtic influences, with the purpose of bringing that Church under the rule of Rome as well.