There will always be, it’s become clear, one more WinstOn Churchill story to tell: one more slant on a weekend, a summer, a year in the life of the 20th century’s most formidable leader, a man whose history includes two world wars and speeches so glorious that future dramatizations were all but inevitable. But what happens when the story being told feels emotionally false and factually bogus? Churchill, a new drama starring the great Brian Cox, is so full of movie clichés and high melodrama that it’s sometimes hard not to giggle — and one should never laugh at the prime minister.

It is early summer, 1944. The Allies’ June 6 D-Day invasion of Normandy is days away, and Churchill is determined to stop it in its tracks. Standing on an English beach in the opening scene, the great man literally sees the sea foam turning red, just as the seas are said to have run red with the blood of soldiers during the disastrous Battle of Gallipoli, a World War I campaign that Churchill championed and that led to some 40,000 Allied deaths.

Determined not to make the same mistake twice, Churchill scoffs when presented the D-Day plans by General Dwight D. Eisenhower (John Slattery) and England’s Field Marshal Bernard Montgomery (Julian Wadham), both of whom all but roll their eyes at the excitable prime minister. Conventional wisdom tells us these plans were years in the making, but the script — by first-time screenwriter Alex von Tunzelmann, a young historian who also writes regularly about the truth-fudging in historical dramas — suggests that Churchill is seeing them for the first time. Alarmed at the idea of a potentially disastrous amphibious assault (as was Gallipoli), he orders his men to draw up plans for an Italian invasion, a command his staff, who treat the old boy like a doddering fool, ignores.

Movie critics are not historians (and shouldn’t pretend to be), but it’s hard not to doubt a film that depicts Churchill bad-mouthing the D-Day invasion three days out. And who knew that the prime minister’s wife (Miranda Richardson) felt so neglected in her marriage that, even with the invasion clock ticking, she packs her bags to leave? Or that she tried to slap Churchill to his senses? Or that it took a speech by a secretary (Ella Purnell) with a soldier fiancé to shame the clinically depressed leader into getting off his duff and doing his job?

And so it goes. The folks behind Churchill deserve the grief they’re destined to get from WWII purists, but the film has at least one memorable moment (maybe two, if you include the bit with the hat). At midpoint, King George VI (James Purefoy) shows up to decline in person Churchill’s invitation to witness the Normandy invasion from aboard a British warship. In real life, the king wrote the prime minister a letter (two letters, actually), but turning those words into a speech — beautifully delivered by Purefoy — is screenwriter fact-juggling at its most pleasing and most forgivable.

Cox’s delivery of Churchill’s “We will fight on the beaches” D-Day speech surely ranks among the best, but it’s a problem when a narrative feature’s most powerful scenes are drawn from historical text. Cox deserves better, but he nonetheless cuts an imposing figure — and an oddly soothing one as well. Maybe it’s just me, but even a doubt-filled leader is preferable to a soulless one, which may be why Churchill, flaws and all, could be just the tonic America needs as this long, nerve-jangling summer begins.