The United Kingdom cannot be reasonably said to have been a democracy in the time of the American Revolutionary War or even a hundred years afterwards; at most it can be said to be semi-democratic or proto-democratic. Until the late 19th century the House of Lords was more powerful than the House of Commons, and even the House of Commons was elected only by the rich for much of the 19th century. It was what could have developed into a representative democracy, and did, but it was not a democracy yet. Even royal interventions in politics, bizarre as the idea may seem now, were not made as powerless as they are now until the time of George V, or arguably even as late as the Edward VIII abdication crisis. The UK is dangerous to the non-existence of representative democracy because of what other things its political system, which included representative-democratic elements on a national scale in a great power, could have inspired, not because of its political system in its own right. If one wants representative democracy to not exist, it is convenient for the Parliament of Great Britain, and its earlier English equivalent, to not include a House of Commons where the lowborn (albeit only wealthy male property-owning ones) could vote for representatives to a national assembly; even though this body was distinctly the weaker part of Parliament for most of its history and there were franchise restrictions that made it very un-democratic, Parliament as a whole did rule, and for the very idea of representative democracy to not become so widespread as it was in OTL it would be better for it not to happen at all.
If you don't have a history of such assemblies in England you're not going to get the colonial assemblies in the English colonies in North America either; it may look a lot more like French or Spanish America, and it may have a tradition where political power tends to be held by hereditary monarchs and aristocrats and appointed governors with the help of wealthy land-owners and the army. I would argue that England and the Netherlands, as the major colonial powers whose political systems included predecessors to representative democracy, are the things that need to be changed for this scenario, ideally. Without the Netherlands and England, proto-representative democracy (probably still for merchants with a very restricted franchise) could very easily remain a bizarre phenomenon of a few city-states, designed purely for the benefit of merchants and considered impractical to ever implement on a national scale (an example which ancient history would validate to an extent).
I do not believe that revolutions would be likely to create such a system as representative democracy from scratch, if there were not already an existing precedent of how such institutions could work on a national scale. The entire way a revolution works is that a group of people use violence to overthrow the state when they disagree with its decisions, usually with a charismatic leader who then takes control and establishes a new authoritarian state. (Things are somewhat different if the pre-revolutionary state already had significant democratic elements, as in the American Revolution, which was essentially to empower one existing part of the government, the colonial assemblies, at the expense of another existing part of the government, the governors answerable to London and the British courts and Parliament.) Sometimes, rarely, this results in the leader giving up his power and establishing a democracy; and when it does, it's usually where there are already existing democratic elements. Usually, it results in the leader deciding that he quite likes having all this power and would rather keep it. Setting the precedent that people can violently overthrow the political order if they disagree with it doesn't lend itself to peaceful toleration of opponents and letting them have power at times, which is a key part of democracy. The French Revolution served to create representative-democratic institutions modelled on, albeit improved from, existing representative-democratic institutions elsewhere in the world. The idea that a political system existed long ago, thousands of years ago, could not help in the same way as an already existing example did. I would reject the argument that the supposed great success of classical democracies would inspire them anyway. Not only were those states thousands of years dead—so almost no-one would have even heard of them—classical writers tended not to have nice things to say about the democracies of their time; lots of the Greek philosophers whose writings inform us of that era despised the Athenian system (to be fair, in part because the Athenian system wasn't very nice to a lot of philosophers—the death of Socrates comes to mind), and the Roman Republic was generally less stable, weaker and less prestigious than the Roman Empire. As for the idea that the ideal of representative democracy could be come up with out of nowhere, without precedent ancient or modern, I would reject that too; look at the record of OTL with people coming up with new ideologies out of the blue and then those ideologies rising to power in revolutions, and we get people like Lenin and Mussolini; such ideologies naturally lend themselves to small revolutionary cliques with strong centralised leadership, as indeed revolutions do in general, because a revolutionary state (by which I mean one that seeks to create an entirely new political order, not merely shift parts of an existing political order around a bit by strengthening some parts at the expense of others) usually has to have a centralised chain of command to implement the radical changes it desires to.
I should clarify that my solution doesn't quite fulfil the terms of the OP because, although representative democracy would not be a prominent political system by the modern day, it also wouldn't be widely prominent in the 1700s and 1800s; it would just be something that never really got anywhere at all. Once representative democracy has already been widespread, it's rather more difficult to put that genie back in the bottle, though it can be done; in particular, inter-war Europe is full of examples of representative-democratic states turning authoritarian under heavy economic distress, and a WW2-esque war between representative-democratic states and authoritarian ones of a particular ideology, if you take away the USA as an extremely powerful and effectively un-invadable representative democracy, could imaginably have ended in victory for the latter.
Getting rid of nationalism, I would go so far as to say, is outright impossible, but representative democracy…? I think not.
