Generally speaking history in UK schools isn't taught chronologically, it's taught thematically, and as you progress through school you deal with more sophisticated themes and concepts in the later years.

You can take a look at the English history curriculum for 11-14 year olds here actually, but bear in mind this is just for England and doesn't apply to the rest of the UK. As you can see it is actually suggested that the Revolutionary War, amongst other things, be a study in ideology, the nature of political power, or empire-building (or losing).

Studying the American Revolution in this way wouldn't be a chronological timeline of key dates and notable individuals, but instead it would be taken as an example of the influence of Enlightenment thought on the Western world. Less Paul Revere, more Thomas Paine.

Beyond 11-14, what you study isn't determined by a national curriculum but your school will adopt one of a choice of courses set by a number of independent 'exam boards', who write and grade the exams and establish the curriculum to be followed.

No major exam boards offer a course on the Revolutionary War at either 14-16 or 16-18, but it's likely to be mentioned in passing at least in several popular courses. Many schools teach The American West: 1840-1895 - have a look for yourself at the kind of thing studied. It's mainly Manifest Destiny, the expansion of the railways and the conflicts with the natives. I would imagine any course on the American West would be preceded by a crash-course in early American history - the Declaration of Independence et al, which would be non-essential but useful, and totally at the discretion of the teacher.

I, and I imagine thousands of others, studied the French Revolution at 16-18, and of course the American Revolution plays an influential role in the ideological and economic background of 1789 and so it featured fairly heavily at the beginning of the course - a student will be taught the war bankrupt France, thrusting it into an economic crisis, and the experience of French troops and key individuals like Lafayette were important in spreading republican and egalitarian ideologies amongst the French participants.

It's not that the war was unimportant, it's just that it fits in rather awkwardly considering how history is taught here. Want to learn about republicanism? We have the Civil Wars, Cromwell and the Restoration. Want to learn about struggles over sovereignty? We have the Glorious Revolution. Want to learn about the Enlightenment? We have the French Revolution. Want to learn about empire? We have the East India Company.

You can see why the Revolutionary War ends up quite far down the list!

Posted this before but I'll put it in here again for reference, although it's much along the same lines as /u/splendourfalls

It's barely taught in the UK, there's just no room for it in the curriculum. Instead our modern curriculum tends to focus on an uber fast blast through Greece, Rome, Anglo-Saxons, Norman Conquest, some Medieval England, Tudors and then Victorian Britain (usually through social history) then the briefest of mentions of the World Wars. Alongside this is world history, which tends to be picked for political reasons. For instance I did Nazi Germany, American Civil Rights, Arab-Israeli Conflict and Apartheid South Africa. At GCSE level (14-16) the schools will have flexibility in what they teach from a selection of modules as /u/splendourfalls mentioned but they usually tend to pick subjects that have political impact such as the Middle East, Gender politics, Nazi Germany or a race related issue such as Apartheid South Africa or the Slave trade. The debate over whether we should be using history in this way or teaching the history of Britain is one that has gone on for a long time. For instance the British Empire barely features aside from in passing, which annoys a number of people from Conservative backgrounds.

Once you get out of school and hit Sixth Form/College it opens up a little and there's more chance of in depth study. For instance I did Britain 1815-1914 and Russia 1815-1990. Most schools at this level will have a choice between 8-10 subjects at this level and it's entirely down to the school what is taught. These subjects change every few years, I've seen the American Revolution in one prospectus but it's not a common thing and it's definitely not an emphasised thing. Most people who have been lucky enough to get taught the subject before Uni will have got it at this stage.

Finally it's at University level where you'll find the Revolution taught properly although again it's spotty depending at what university you're at and often it forms a small part of a generalised American history course. During my 16 years of education, it took me until the final year of my undergraduate degree to do the Revolution and then it was because I picked NYC during the Revolution as my dissertation topic. However I knew people who took Early America based courses, which included the Revolution.

If you're actually lucky enough to learn it then it's taught in a fairly balanced way from what I've been told, not the exaggerated way it is in America sometimes. Reasons for the Revolution are discussed both pro and contra, the state of the colonies are discussed, as are the Loyalists (who are as I understand it rather missing from the American story). The actual war is taught how it happened. The British won most of the battles, quickly adapted to the situation, contrary to the idea of bumbling redcoats being shot by snipers with rifles, but couldn't win the war because of the sheer scope of what they had to occupy, the politics at home and spotty Loyalist support.

tl;dr: It's not really taught, if you're lucky you might get it at 16-18 level. It's taught to a greater degree at undergraduate level but again it's at the whim of who happens to be teaching at your institution. The actual teaching is fairly balanced with no overt British exaggeration while dispelling much of the American myths of the conflict. It hasn't been considered important by our previous governments, although the current education secretary (Michael Gove) seems to be more interested in it and more 'traditional' topics that past ones.