Are cycle lanes a good idea on the A2680?

Using the A2680 a few times a week, I thought that one day it would be the scene of a tragic accident.

Motorists travel down the middle of the road overtaking whilst oncoming traffic is travelling the other way.

My idea would be to add cycling lanes on both sides of the road which would make it safer for bicycles and also keep traffic towards the middle of the road so it 
makes it much harder for motorists to overtake and travel down the middle of 
the road.