The ideas of self government originally came from 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.
There were three ideas that the colonists brought with them about government when they traveled to the new world from England. These ideas included one of an ordered government, limited government and representative government.
Puritans
duogie
She believed in education and new ideas. She never married because she knew that if she did, her husband would take over ruling and do a terrible job.
There were three ideas that the colonists brought with them about government when they traveled to the new world from England. These ideas included one of an ordered government, limited government and representative government.
England
No, England did not take over india
They Borrowed the English Bill of Rights
how long does it take to sail from Pakistan to England
The movement split churches. It also stirred up ideas of individual worth, equality, and the right to challenge authority. These ideas prepared the colonists to break away from England.