Who created parliamentary democracy?

It evolved over time. Both Britain and Sweden developed it independently and both obtained it around the same time.

In the case of the UK, the English monarchs had been slowly restrained by parliament (and before that, the nobility) since 1215 and King John's forced signing of the Magna Carta, and over the centuries the role of the King was decreased over and over again. Starting from 1295,we had parliament and the King used to put all his officials into parliament (via a peerage or by getting them elected) which essentially created the principle that all ministers in government had to be accountable to parliament.

So, as time went by, parliament asserted itself again and again, actively deposing King Richard II in 1399, until the 17th Century when the Kings we had imported from Scotland earlier that century (used to a more docile parliament) tried to rule without parliament - this started a civil war and eventually we cut off this King's head (King Charles I).

After about a decade of supposedly 'republican' rule (actually a dictatorship) we got King Charles I's son back to be King (King Charles II) and he knew his place. The King, at this point, formed policy and appointed ministers to carry out his decisions. After that King died, we got another one (King James II) who was quite frankly very authoritarian and Catholic to boot, so we invited William, Prince of Orange, to invade, although hardly any fighting took place - most of the army sided with William. So when King James II escaped, parliament declared that he had abdicated and gave the throne to King William III and Queen Mary II; protestants who would rule through parliament. That was the real beginning of the principle that parliament is sovereign, not the King.

Then, in the 18th Century, the succession fell to the Hanovers, a bunch of Germans who didn't speak good English and had little interest in domestic politics. So, that was when we got our first 'prime minister' (even if the name didn't get used until much later - his title was 'first lord of the treasury') - Sir Robert Walpole.

So now, the King isn't taking much interest in politics, government is delegated to the prime minister with only very vague thoughts on policy coming from the King (though they did do slightly more on foreign affairs). The prime minister still had to keep the King happy as well as parliament though.

The beginning of the end for any royal role in politics began with (believe it or not) the American Revolution. The King refused to sack the prime minister Lord North or let him resign even though he himself had admitted he was no good at winning the war; he was eventually forced to by parliament. And so began a fifty year period of increasing agitation with the unfair system of election (pretty much unchanged since 1429), corruption in parliament, and royal battles with parliament. In 1832, the Great Reform Act signalled the end of royal interference as parliament was now truly accountable to the people, and the prime minister had to keep parliament happy rather than keep the King happy because parliament could strip him of his position while the King couldn't without being forced to abdicate afterwards.

So, I suppose you could say it was principally created by the 25 Surety Barons who forced King John to sign the Magna Carta, Oliver Cromwell who was in charge when they cut off King Charles's head, King William III and Queen Mary II and the 513 MPs and 82 Lords who put him on the throne, King George I and our first prime minister Sir Robert Walpole, King George II and King George III, and finally Lord Grey who proposed the 1832 Reform Act.