British equivalent of the American take a look. There seems to be a British fondness for verbal idioms that start with have a–for example, have a go at it (U.S.: give it a try); Are you having a laugh? (the Ricky Gervais’ character’s catch phrase on the TV show “Extras”); and this headline from NOW Magazine: “Charlotte Church: I was having a wee, not sex in embarrassing snaps.” (To make sense of this quote, insert comma after “sex” and know that “snaps” means “photographs” in British tabloid English.)
A Google Ngram of American use of have a look (blue line) and take a look (red line) from 1850-2008 shows they were more or less equally popular until about 1960, when have dropped and take took off. Like many Britishisms, the American use of have a look has steadily and significantly increased in since roughly 1980.
Devotees of Candace Bushnell–a journalist who looks like Suzanne Somers with a polo-club membership–approach her writing the way they might a car wreck or a Peter Greenaway movie: they know it might repel, but they are forced to have a look. (Ginia Bellafante, Time, August 12, 1996)/Complex date calculations aside, we will have a look at a handful of the companies who have withstood the test of time, both at home and abroad. (San Francisco Chronicle, July 18, 2011)
notoneoffbritishisms.com 
I think the difference between British and American use breaks down into several parts. In the US we’re likely to use “Take a look” at whatever, as an imperative. With have a look, the semantics would probably dictate using “have a look” interrogatively, as in: “I just finished my report. Would you have a look at it?”
I find American English to be more literally accurate, e.g., you take a look, rather than having, i.e., owning, a look. But for me the slightly less literal sense of British English makes it more fun; the ambiguities leave more room for context & delivery, ironic or not.
I’d be interested to know what the ‘official’ Canadian usage is. I say “have a look” here in Canada’s London (Ontario).
I’ve also noticed the Brits say, “have a lie down” or “have a walk”. Americans would say, “I’m going to lie down” or I’m going to go for a walk. Americans verb it, Brits noun it.