It is now routine, in surveys of best-ever TV fictions, for US series screened during the last decade – including The Sopranos, Breaking Bad, Mad Men and The Wire – to slug it out for gold, silver and bronze, while Britain's main hope of making the podium comes from productions that date from far back into the last century, such as The Singing Detective, Boys from the Blackstuff and Edge of Darkness.

Some argue, though, that Britain is too submissive to the legend of a new American golden age of televisual imagination and this may be a good time for the fightback to start, as the first half of this year has seen the launch of three of the most lauded and talked-about dramas made in the UK in recent times.

Line of Duty (February, BBC2), Happy Valley (April, BBC1) and The Honourable Woman (July, BBC2) have set levels of writing, characterisation, acting and filming that have been the envy of US TV. At the most recent annual showcase in Los Angeles, where broadcasters from around the world screen teasers for new dramas, BBC executives received covetous compliments on Happy Valley, just as ITV delegates did in recent years for Downton Abbey and Broadchurch.

Maggie Gyllenhaal as Nessa Stein in The Honourable Woman. Photograph: Des Willie/BBC/Drama Republic

There is also evidence that audience enthusiasm for British dramas has increased. Happy Valley, Sally Wainwright's six-part drama in which a kidnapping exposed layers of grief and betrayal in two families, received record audience-appreciation scores for a BBC1 drama. And Line of Duty – Jed Mercurio's police-corruption thriller – matched the instant-classic status of over-there shows such as Breaking Bad by being chosen among BBC2's greatest achievements of the last 50 years even though it entered contention at the last possible moment. ITV's Broadchurch (shown last year) and Channel 4's Utopia – Dennis Kelly's violent counter-history of Britain, which has just returned for a second series – would also rank among those broadcasters' historic highlights.

So has British TV drama at last woken up and smelled the coffee? A common risk in measuring one area of culture against another is that it is hard to achieve comparable samples. Drama of the 16th or 19th centuries will tend to seem superior to theatre of the 21st because, through a process of Darwinian winnowing, we have seen only the best work from their time but get to see the worst of ours.

Danny Cohen, director of television at the BBC, argued recently that the alleged inferiority of British TV fiction depends on an equally false opposition. He complained that some viewers and critics who see only the very best American products then set those standards as the benchmark for judging a full UK schedule that will inevitably feature the unspeakable amid the unmissable. As a result, "consumers who have a larger voice in Britain's cultural dialogue than the average family" often find home products wanting. But Cohen believes that a properly handicapped race between the best from each stable would result in a freeze-frame finish.

His arguments are persuasive, but, for me, there remains one fight that the Americans will still generally win: originality. For all the freshness of execution shown by Sherlock and Downton Abbey at least in its first series), both were variations on established franchises: the novels of Arthur Conan Doyle and the English country house drama (Upstairs Downstairs, Gosford Park). And admirable as they are, Line of Duty, Happy Valley, The Honourable Woman and Utopia are all conspiracy thrillers, featuring cops or spies or both. Even Doctor Who – the BBC's most globally successful drama at the moment – is a revamp of a drama that began in 1963.

New wine in old bottles can still be vintage, even in the TV vineyards of LA and New York: David Chase's magnificent The Sopranos (HBO, 1999-2007) was a recognisable descendant of earlier mafioso yarns such as The Godfather. However, other recent hit shows from the US – such as Matthew Weiner's Mad Men (AMC, since 2007) and Vince Gilligan's Breaking Bad (AMC, 2008-13) – more or less invented their own genre.

Mad Men. Photograph: Everett Collection / Rex Feature

Before Mad Men, most American TV narratives were contemporary in setting, partly because the nation's networks had no equivalent of the heritage reflex that has led the BBC – especially when the licence fee is coming up for renewal – to remake adaptations of the novels of Charles Dickens and Jane Austen in rotation. But, when American TV decided to look back, it, crucially, went for inspiration not to the shelves of American literature but to the media archives, luxuriantly recreating the clothes, smoking, Kennedy iconography and posters of the 1960s through choosing a Madison Avenue advertising agency as the location.

It can be seen as symbolic that, whereas a British TV period piece is usually set in the 1800s or 1900s, the American drama Tardis set its coordinates for the mid-20th century; and, while an obsession with Austen and Dickens has often spared viewers from prickly issues such as racism and sexism, Mad Men deliberately dramatised a pivotal era of ideological shift. The rapidity with which UK commissioners attempted anglicised imitations of Mad Men – such as The Hour (BBC2, 2011-12) and Breathless (ITV, 2013) – is explosive ammunition for those who suggest that TV drama here is culturally cringing.

Mad Men – along with Breaking Bad – also displayed a courage of characterisation that was unfamiliar in our schedules. Don Draper (Jon Hamm) of Mad Men and Walter White (Bryan Cranston) in Breaking Bad are fundamentally amoral, though in other ways attractive, people. Draper is a philanderer and liar with an encyclopedia of terrible secrets, while White makes the improbable journey from school science teacher to psychopathic baron of a drug cartel. There are mitigating circumstances in each case – Don suffered a terrible childhood, Walter has terminal cancer and a dependent family – but the consensus among British dramatists is that drama bosses in London would have fretted that such protagonists were insufficiently "likable" to engage viewers.

However, such views may, under influence from America, be loosening. DI Lindsay Denton – brilliantly played by Keeley Hawes in Line of Duty – breaks heads, rules and bodies with a brutality unprecedented for the female hero of a mainstream British TV police procedural. In the same way, while there was a rare psychological complexity to Sgt Catherine Cawood – extraordinarily portrayed by Sarah Lancashire in Happy Valley – her domestic and professional failures were rooted in circumstances (divorce, bereavement) that encouraged the audience to warm to her.

And yet, British TV has an unreachable lead in one area: whereas the major roles in all of the fabled recent US shows are male, the central figures in Line of Duty, Happy Valley – and The Honourable Woman, starring Maggie Gyllenhaal – are women.

Angel Coulby in Dancing on the Edge. Photograph: BBC/Ruby Film and Television

Not that British TV drama hasn't learned from America. Television in LA popularised the job of "show-runner": an individual who not only creates but also creatively controls the look of the show, as Weiner does on Mad Men and Gilligan on Breaking Bad. Historically, the British model was that one person – for example, Dennis Potter – would write scripts and then hand them over to a producer. The British industry has always been resistant to the idea of the writer-producer-director hyphenate, partly due to a feeling that Potter's work deteriorated as he assumed more power. Subsequently, while Stephen Poliakoff's Shooting the Past and The Lost Prince made a strong case for multitasking, his more recent Dancing on the Edge was cited by those critical of the practice. So, until now, the American model of show-runner existed mainly at Doctor Who, where it was accepted that an all-powerful auteur – first Russell T Davies and then Steven Moffat – was the only hope of salvaging the brand. This year's three BBC hits, however, have been substantially run by one person. Hugo Blick writes, directs and produces The Honourable Woman (as he did its predecessor The Shadow Line), while Wainwright has increasingly taken on more responsibility for her scripts: on Happy Valley, she had a producer credit and directed an episode. Jed Mercurio produced and wrote Line of Duty.

So, in quality and structure, UK and US drama are now ever closer. But a final note of caution should be sounded, echoing Cohen's warning about the importance of comparing like with like. While the standout UK pieces of the last two years were all screened on mainstream channels, the modern US masterpieces are the creations of niche subscription services or, in the case of Netflix's much-discussed House of Cards, through video streaming that requires no TV set.

While subscription networks or streaming sites have liberated American fiction-makers from the conservative pressures of regulation, advertisers and morality campaigners, writers and producers, here we still usually have to work within parameters set by Ofcom, the culture secretary and newspapers. The new series of Utopia provoked a Mail on Sunday front page about the use of the murdered MP Airey Neave in a fictional conspiracy plotline, so imagine the reaction if a British terrestrial network had screened something as transgressive as Breaking Bad. The next challenge is to find protected experimental spaces – as exist to some extent with BBC3 (Being Human) and E4 (Skins) – that encourage shows that are not intended to be for everyone. If we are to achieve absolute equality with America, drama departments here may need to hang up a sign that reads: "No cops, no spies."

• The Honourable Woman continues on Thursdays at 9pm on BBC2, Utopia on Mondays at 10pm on Channel 4. Line of Duty and Happy Valley are available on DVD.