"This site is generated from information from Hansard, the Official Report of debates in Parliament. Information presented here is generated from the publicly available XML files. Material on this site remains under Parliamentary Copyright. Within these copyright constraints, you are encouraged to use and to explore the information provided."
This site has debates from the UK House of Commons (I don't think The Lords is included) that go back at least to World War II. The purpose of the site is to raise public awareness, however it is useful to the historian as a source.
These medieval parliamentary records have just been released. They're part of the 'premium content' section but it's only 30 pounds per year to access so might be worth it.
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British History Online
British History Online is the digital library containing some of the core printed primary and secondary sources for the medieval and modern history of the British Isles. Created by the Institute of Historical Research and the History of Parliament Trust, we aim to support academic and personal users around the world in their learning, teaching and research." Syas it all, really.