The British-English phrase gizza job (also gizzajob, gissa job and gissajob), which means give us [i.e., me] a job, is used as a plea for employment.

Referring to the desperation bred by unemployment in the early 1980s, this phrase was popularised—if not coined—by the Scouse screenwriter, playwright and novelist Alan Bleasdale (born 1946) in Boys from the Blackstuff, a television drama series of five episodes, originally broadcast on BBC Two from 10^th October to 7^th November 1982, and repeated on BBC One nine weeks later. Set in Liverpool, a city and seaport in north-western England, this series depicts five characters struggling to survive and come to terms with the insecurity of life on the dole.

Specifically, it was through the character of Yosser Hughes, played by the English actor Bernard Hill (born 1944), that Alan Bleasdale introduced the phrase—as explained by Roy West, TV Editor, in a portrait of Bernard Hill published in the Liverpool Echo (Liverpool, Merseyside, England) of Wednesday 24^th November 1982—the earliest occurrence of the phrase that I have found is from this portrait:

“Yosser Hughes is harder than Souness,” chants the Kop*. “Gizza job. Go on, gizza job,” mimics every public bar comedian on Merseyside. “I could do that,” chirps a little lad, peering over the Anfield crush barrier as Sammy Lee goes to take a corner.
Yosser Hughes is Liverpool’s latest folk hero. And at the moment there’s no escape from him and his catch phrase. This hypnotic nut case of a character from Alan Bleasdale’s TV drama series The Boys from the Blackstuff has captured the imagination of Merseyside — and beyond — over the past few weeks.
Driven insane by his futile efforts to find a job, he’s become a symbol of the desperation bred by unemployment.

(* At Anfield, home ground of Liverpool Football Club, the Kop designates a high bank of terracing where spectators formerly stood. This term originated in Spion Kop, the Afrikaans name of a hill near Ladysmith in South Africa, scene of a battle in the Second Boer War (1899-1902), in which troops from Lancashire led the assault—Liverpool then being part of Lancashire.)

The second-earliest occurrences of the phrase that I have found are used attributively; they are from the following letter, published in the Liverpool Echo (Liverpool, Merseyside, England) of Tuesday 7^th December 1982:

Yosser could bring hope to the jobless

Maybe out of work Yosser from the “Blackstuff” may just be what the unemployed of Liverpool are looking for to put them back on the map, and also give work to some of the unemployed.
How about someone re-opening one of the empty factories in Skelmersdale to manufacture Yosser tee shirts, mugs, car stickers, key rings and Gizza Job mugs and tee shirts?
There must be lots more Yosser goods and Gizza Job goods that could be manufactured, so come on Liverpool, can we do it?
One day we may even export them abroad!
Mrs. H. Phillips, Birkdale, Southport.

The following from the Evening Express (Aberdeen, Aberdeenshire, Scotland) of Tuesday 18^th January 1983 bears witness to the popularity of both Yosser Hughes and his catchphrase:

BBC 1 highlight

In BBC 1’s “Nationwide” tonight James Hogg reports from Liverpool on the cult that has grown round Yosser Hughes, the fictional character from Alan Bleasdale’s “Boys from the Blackstuff” drama series, first shown last autumn on BBC 2 and currently being repeated on BBC 1.
Yosser is obsessed with the need to find work so that his children are not taken into care — an obsession that degenerates into madness. “Nationwide” shows how Bleasdale’s combination of the stark reality of unemployment on Merseyside with a grim Liverpudlian humour has struck a strong chord with the local people.
“Gizza job, go on” and “I can do that” have passed into the vernacular, and three underground Yosser disco records are played in the clubs and pubs.

Both the earliest occurrences that I have found of the phrase gizza job without reference to Yosser Hughes are from the Liverpool Echo (Liverpool, Merseyside, England):

1: Thursday 17^th February 1983:

Chance for soccer hopefuls to kick dole into touch

A scheme has been announced to blow the whistle on the Scousers’ sad cry of “gizza job”.
For unemployed boys with “golden feet” have been told to aim for a place in professional soccer.
The new football training scheme has been launched in Birkenhead, where the 30 per cent jobless total is 13,500 with only 166 vacancies—a town which has produced stars like Dixie Dean and Steve Coppell.

2: Tuesday 26^th April 1983:

‘Gizza job’ plea as Gabriel tackles VIPs
By Carolyn Taylor
Unemployed Liverpool building worker Gabriel Muies went to the top to-day and demanded: “Gizza job”.
He spied his chance at to-day’s ceremonial sod-cutting on the new Wimpey site in Toxteth to ask for work.
After the speeches from Wimpey chairman Mr. Nelson Oliver and City Council leader Sir Trevor Jones, he bent the ear of Wimpey’s Regional Director Geoff Slater.
Then he tackled the chairman and Sir Trevor in a bid to end his two years on the dole.
The impromptu job hunt happened when Mr. Muies gatecrashed the V.I.P. party.
Mr. Muies lives in nearby Loudon Road which bounds on one side the new Windermere Park estate which will consist of 227 new homes.
[…]
Later, Mr. Slater said the company would be recruiting, and Mr. Muies would certainly be considered for work.

Gizza job . . . Mr. Miues [sic] tackles Wimpey regional director Geoff Slater.—photograph from the Liverpool Echo (Liverpool, Merseyside, England) of Tuesday 26^th April 1983: