In 1610 the Case of Proclamations definitively established that the king could not make law by himself, but only together with Parliament. It also established that the king only had the powers which had been recognized up to that point and could not create new ones without parliament.

But well before that the common law (the law as interpreted by the judges of the royal courts) established that the king could not impose new taxes without parliament. This is stated in the magna carta. In the views of many monarchs (e.g. Elizabeth I) the only real point of a parliament was because the monarch wanted money. Parliaments were summoned infrequently. Elizabeth the first summoned only 13. She summoned one parliament to ask it if she should execute Mary, Queen of Scots. The other 12 she asked to impose new taxes. Read more here.

Although this was the law well before the 1600s it was not confirmed in statute until the 1688 Bill of Rights:

That levying Money for or to the Use of the Crowne by pretence of Prerogative without Grant of Parlyament for longer time or in other manner then the same is or shall be granted is Illegall.