Small Island on BBC One

Jamaica is a small island. Britain's not much bigger, thinking about it.

The discovery of that fact by two Jamaican immigrants of post-war Britain is the crux of this two-part BBC drama adapted from Andrea Levy's novel. What they also have to learn is something those of us that have lived here for a while could have told them from the start: Britain ain't all that great.

In their defence, Hortense and Gilbert (Naomie Harris and David Oyelowo), have come over as part of the SS Empire Windrush migration from a Jamaica that still recognises imperial Britain as the 'mother country' and have been told countless stories about how wonderful (though cold) the place is. Electric lights in every room! Visits to the King in Buckingham Palace! Yeah...

So partly we're watching the gradual demolition of dreams in the dreary London boarding house and streets of the late 40s/early 50s. Partly, we're trying to ignore the Desperate Housewives-style voice-over that trots of proverb-sounding bits of trite wisdom (stuff that's okay on DH because none of that show can be taken seriously anyway). Luckily, Harris and Oyelowo don't let it get too mawkish, and their early innocence is touching and plausible. They aren't exactly naïve, just unworldly and unprepared for the reality of a post-war 'mother country' that – as Gilbert says – doesn't know where her children live.

My church in Wolverhampton has several members who were onboard the SS Empire Windrush, and I think it's this familiarity with the cadence of the Jamaican accent that made me wince whenever one of the Jamaican accents here went off towards America or somewhere else. Shaun Parkes – a fine black British actor (better known for playing British-Ugandan characters) – carries it off well, but Oyelowo occasionally sounds like a caricature Jamaican. Harris has moments where she could be from America's east coast (which is odd because her mum's Jamaican) – were there no genuine Jamaican actors the BBC could call on?

The ingratitude and blatant racism of the locals is also marked, and sits rather uncomfortably with an audience reminded again and again that the male 'darkies' here are all men who served in the RAF against Nazi Germany and are now full British citizens like their paler associates. That doesn't seem to matter to the cockney postmen who subject Gilbert to a 'noble savage' moment on his knees.

But what's interesting is that, while Small Island lays stress on racial difference, the sexual discrimination of 40s/50s Britain (and Jamaica) is left largely untouched. It's all very well to pull on our heartstrings about the poor RAF men derided as monkeys by their new Royal Mail colleagues, but what of the wife they've left in the boarding house with no idea how to cope in this strange, cold land? It's a classic case of bullying when the disgraced Gilbert comes home to treat his wife to an angry outburst that she can't possibly understand, having not seen his day at work. Time and again, these Jamaican men complain of being oppressed or looked down upon, while treating their women in a strikingly similar way.

It's not all gloom though. Landlady Queenie (Ruth Wilson) gets to have her fun with the RAF and is an extremely progressive female figure. She sleeps with who she wants, she has economic independence, and she bosses her husband, Bernard (Benedict Cumberbatch), around threatening to throw him out in favour of her Carribean lodgers. Well, good for her. Sort of. It would be if she hadn't fallen for completely the wrong man.

Michael Roberts (Ashley Walters) – the Jamaican airman prone to copping off with married white women – doesn't do any favours for the stereotype of black men. As the father of Queenie's illegitimate child he lends some weight to white reservations about hiring black men in places that employ white women. What's worse is that the two thoroughly decent men (Bernard and Gilbert) are always left to pick up the pieces that he leaves behind. Gilbert is often mistaken for him, to his and everyone else's confusion/dismay – as Gilbert says, he's not the only black man in England, but everyone else seems to forget that. While Gilbert takes the reproachful looks on suspicion of impregnating Queenie (adultery twice over), the real father is swanning off to Canada, leaving the woman who has never really loved anyone else.

So we can learn that neither island is the idyll we may have thought it, and that you've got to work at your dreams if you want them to come about. It's not always comfortable for a white audience to hear the sorts of things said to the Jamaican people; there's a smug air of adult to child throughout, and sometimes a genuine fear of physical contact in case the black skin rubs off. But there's also the reminder that without such immigrants Britain wouldn't have made it through WWII never mind the ten years that followed.

We as a nation (a multi-ethnic nation, all of us that appreciate the freedoms won in the 1939-45 war) should be grateful to the passengers of the SS Empire Windrush and those that followed.