I would save him for a sequel. Have the first Captain Britain film set in the time of Camelot where it can feature the Black Knight. They can have him in his original lionheart costume. He can get killed by the White Rider and then brought back to life, whereupon he can get the Excalibur costume.
Then for a sequel they can move it to the 1940s. Yes, it would be copying Wonder Woman's model of moving through different decades, but that's fine. As for how Captain Britain survives that, well I don't know how he appeared in different decades in the comics in the first place. Maybe it was time travel or he was only temporarily there?
Didn't Marvel already have the equivalent of the Union Jack character in Captain America the First Avenger? I think it was just his alter ego, but he never suited up.