How course it could have worked there are just some factors you have to look at.

1 The Germans would have too win the Battle of Britain which is possible like Kagemusha said the Germans would have to concentrate on Airfields and Industry not terror bombing London. Which would take out the ability to produce airplanes, tanks, and machinery.

2.You need to find a way to transport enough troops across the Channel to take out the British forces on the island which will be a problem.

3.I dont know what you should do about the RN I have no idea.

4. Or like Kenshin said to dam up the whole English Channel and just drive across.