Do Brits often use 'blag' where Americans use 'chutzpa' (for an extreme degree of impudence, gall)?

The word "chutzpa" (pronounced "HOOTS-pah") took root in American English towards the end of the Nineteenth Century. Originally Aramaic (don't hold me to it: I don't know whether Jesus used it; I doubt it: it's a pretty tacky word, if you ask me), it somehow sneaked into Yiddish prior to landing in the States.

It means - well ... An extreme degree of impudence; gall; ballsy obnoxiousness; in-your-face impertinence; aplomb and confidence - all at the same time. A conversation involving chutzpa would go something like this:

"You owe me twenty bucks."
"Excuse me?"
"You heard me. Pay up."
"But I don't even know you."
"Before you married your wife, she and I went out on a date, and she borrowed a twenty from me, and never paid me back."
"I've been married for twenty years."
"So what? Come on, let's not drag this out. Make with the twenty."

You get the gist. Chutzpa is very useful in a con, long or short, and invaluable in big business, or so people who are more familiar with such matters than myself have assured me on numerous occasions.

Some years ago I read an article in a magazine that was back then regarded as reputable by people who subscribed to it (I didn't - I don't believe in reputable magazines). The author of the article compared American and British English, and mentioned, very much in passing, that the Brits said "blag" instead of "chutzpa."

I don't know. Do they? Do you?

Well I'd suggest that the British historically are masters of the art of 'impudence; gall; ballsy obnoxiousness; in-your-face impertinence; aplomb and confidence' related behaviours. Historically the word would have been 'effrontery', as the OED relates:

effrontery
(ɛˈfrʌntərɪ)
Also 8 effronterie, -ary.
[ad. F. effronterie, f. effronté: see effronted.]
Shameless audacity, unblushing insolence. Also concr.
1715 M. Davies Ath. Brit. I. Pref. 28 By Printing those Orthodox Letters he gain'd the Point of making his own Effrontaries to sell the better. 1720 Welton Suffer. Son of God I. v. 100, I express my Resentment..by the superficial Effrontery..of my Brows. 1751 Smollett Per. Pic. (1779) III. lxxx. 65 The happy inheritance of impregnable effrontery. 1814 D'Israeli Quarrels Auth. (1867) 362 Both as modest in their youth as afterwards remarkable for their effrontery. 1858 Robertson Lect. ii. 58 With blasphemy and unscrupulous effrontery. Hence eˈffronterist [see -ist], nonce-wd, one who displays effrontery. 1776 Adv. Corkscrew ii. 18 He was now become a perfect effronterist.

A 'chap' (at best, but never a gentleman) would be described as having or showing 'effrontery' or more commonly these days (and curiously), 'the effrontery to...' followed by some description of the relevant behaviour or attitude. However, as suggested here, the sort of person using this expression was more likely than not to to be speaking down to the 'lower classes', or to a renegade against the norms of behaviour of the British upper class, and consequently the word 'effrontery' does not readily allow for a person to having pride in having it, or convey any sense of admiration when used in respect of others.

A slightly less pejorative word with a similar sense in British English would be 'brazen', as the OED has it:

brazen
I.brazen, a.
(ˈbreɪz(ə)n)
Forms: 1 bræsen, 2–7 brasen, 4 brassen, 4–5 brasun, 4–6 brasin, -yn, 5–6 brason, 6 brassin, 7 brassen, brazon, 6– brazen.
[OE. bræsen, f. bræs, brass; see -en1.]

3. fig. Hardened in effrontery; shameless.
   1573 [see brazen-face 1]. 1588 T. L. To Ch. Rome (1651) 11 Seeking (after their hard and brazen progenitors) t'establish a righteousnesse..of their owne. a 1639 W. Whately Prototypes i. xix. (1640) 220 A brazen forehead, that is never a whit abashed. 1731 Swift To Gay, I knew a brazen minister of state, Who bore for twice ten years the public hate. 1853 Robertson Serm. Ser. iii. v. 70 The outcast woman whom human scorn would have hardened into brazen effrontery. 1869 Parkman Disc. Gt. West. x. (1875) 124 A rare monument of brazen mendacity.

But noting the usage sometimes concedes a more generous interpretation, as in Mary Beacock Fryer's 'More Battlefields of Canada':

The connection between 'brazenness' and 'chutzpah' is made in William Beusay's 'Boys!: Shaping Ordinary Boys into Extraordinary Men':

... and again in Steven Jacob's 'Rethinking Jewish Faith: The Child of a Survivor Responds':

To conclude, one might compare the relative frequency (in Google Ngrams) of 'effrontery', 'brazenness' and 'chutzpah' firstly in British English, and then in American English:

Someone who might be described as being arrogant, conceited and very self-assured is often accused of being cocky, it's rarely used as a compliment, whereas chutzpah, if I'm not mistaken has an almost sneaky, admiring tone. An Italian would say furbo, which means a smart sly person, one who's not afraid of bending the rules in order to escape a difficult and onerous situation.

A typical British expression is cheeky monkey, often used by an adult when addressing a rude but likeable child. A woman might say this to a man who pays her a heavy, but flattering compliment; or between two friends who gently tease each other.

Does the combination of someone who is cocky + furbo + a cheeky monkey come close to the Yiddish chutzpah? Perhaps. On the other hand, there isn't really a British equivalent, and that probably explains why the Yiddish expression has become part of the American English vernacular.