What 2 ideas did the Commonwealth introduce into England?

No ideas were introduced into England by the Commonwealth. The Commonwealth was established from the British Empire with the Queen being the head. England, being the main member state of U.K, therefore had nothing introduced into it from the Commonwealth opposed to England introducing ideas into Commonwealth member countries. So I'm not sure if this is what you meant, but I think your question should be "What two ideas did England introduce into the Commonwealth?" and in that case I would say that there are a lot of ideas that were introduced, too many to list without having more specific details on what type of ideas you want listing.