In the United Kingdom, what is colloquial for House of Commons? Would you say a member addressed the House, addressed Commons, or would you also say he or she addressed the House of Commons?
Where it is obvious which house is being referenced you could just say the House - with a capital H.
Where distinction is necessary one normally sees the Commons - but remember it always takes the definite article.
You can of course give it its full moniker the House of Commons.
If you are needing to stress that something actually happened in the Chamber, as opposed to somewhere around the members' lobby, offices etc - you could say either in the Chamber or on the Floor of the House.
All of the above applies equally in the case of the House of Lords. Together they constitute Parliament.