There was no Atlantic Wall on Britain's coast in early Summer 1940
It wouldn't have required anything close to the magnitude of Overlord to land 8-10 divisions around the Dover area. Britain's defenses at the time were nonexistant. They didn't have so much as a single tank trap on the beaches. Now imagine how much worse off they'd been without the evacuations at Dunkirk.
Their homefleet was in such a bad state, they were in negotiations with the US to purchase 40 obsolete destroyers to help bolster their capabilities. If you read the historical documents, the British government was petrified in June and July of the Germans jumping the channel. They knew they had almost nothing to stop them with.