’Twas a grim February teatime in West Wickham, south London, when I saw my first parakeet. About six of them, in fact. I looked up from doing the dishes, through the window overlooking the garden, and there they were, where no medium-sized members of the genus Psittacula should be. Half a dozen slashes of the most vivid green imaginable against the brown bleakness of late winter in suburbia. Wholly improbable, wholly mesmerising, wholly wonderful. This was 25 years ago and I’ve been a fan ever since.

They have become a far more common sight since then, of course, as the title of Chris Packham’s latest documentary, Invasion of the Parakeets, suggests. There are now an estimated 15,000 pairs in the UK – the largest population in Europe.

Packham whips through the theories of how they arrived from their native Asia and Africa. Some were released after the filming at Isleworth of the 1951 Bogart-Hepburn vehicle The African Queen. A pair belonging to Jimi Hendrix’s girlfriend were set free in the late 60s as “a gift to peace”. Others are relatives of the half a million animals brought to the UK between 1975 and 2005 when we had a thing for pet parrots and didn’t care too much about caging wild birds or displaying them in the sitting rooms of a dispiritingly cold country.

But that is not his focus. Instead, Packham asks: are parakeets truly invasive? Are they damaging our native birds’ ecology and having a deleterious impact on their populations? Or are they just loud and a bit vulgar? Are we being speciesist towards – or at least engaging in class warfare with – birds?

The naturalist is as cheery, passionate and unsentimental as ever as he gathers facts, figures, evidence and anecdotes from professionals and amateurs with experience of the parakeet population. Individual observers claim that the birds encroach upon nesting sites used by nuthatches, starlings and woodpeckers, ruin fruit crops and defecate all over cars. I’m not sure Mazdas are a native bird species, but I don’t drive, so I am willing to defer to a lot of very annoyed people in Kent.

I give less ground to the guy shooting the parakeets off his feeder with an airgun. I do not consider him armed or dangerous. I think you could do a good “mam face” and grab that stupid thing off him (“Give me that!”) without a moment’s resistance.

Anyway. Among the people looking into these things more widely, the consensus seems to be that parakeets are having no effect on native bird populations, although Tim Blackburn, a professor of invasion biology at University College London, adds a note of caution. It depends on how large a population becomes – and crop-loving birds such as parakeets do not have to make very large inroads into a farmer’s yield to have an effect. “Most of [it] covers costs … If parakeets are stripping 10%, they are essentially changing a profitable enterprise into one that will fail.” Sibylla Tindale of High Clandon Estate vineyard in Surrey has found that playing recordings of birds of prey and the screams of lesser birds being eaten has saved her grapes. Whether this is replicable at scale is not pursued.

Along the way, we are invited to muse upon what qualifies a population as native – 48% of our terrestrial fauna was artificially introduced to our isles – and whether our tolerance for newcomers is evenly distributed. Pheasants and red-legged partridges are imported by the thousand for shooting season on estates (as part of an industry worth £3.3bn to the UK) and survivors go on to gobble up seeds, berries, insects and rare reptiles without anyone getting upset. “Bonkers,” says Packham.

Then there are Canada geese, which I know for a fact have done nothing to add to the sum of UK happiness – and quite a lot to detract from toddler safety and maternal rest in our parks – since they were brought over in the 17th century to entertain berks in royal palaces.

Invasion of the Parakeets doesn’t labour the parallel immigration arguments and attitudes about humans and birds, but rather lets them come to roost gently among the standard nature documentary stuff. It is nicely done. And none of it is about football. For which, as ever, many thanks.