I very much doubt it. Changing the manager won't do anything, the players are just not good enough. But I will say that England played better football than they have in the previous two World Cups.
For England it is too much money, too many foreign players and poor coaching at youth level. Take Arsenal for example, Bacary Sagna is leaving and they are searching for a proven replacement from abroad, even though they have a very good young English replacement in Carl Jenkinson.
And because of the big money young English players are lured to the big teams even though they won't play. Jack Rodwell was a very promising young player but moved to Man City and barely played.