The derogatory expressions loony left, loony leftism and loony left-wing designate a very radical, extreme or fanatical left-wing faction within a political party or the political spectrum. The derogatory expressions loony leftist, loony lefty and loony left-winger designate a member or supporter of such a faction.
—Cf. also loony fringe in ‘lunatic fringe’: meanings and origin.

The expression loony left occurs, for example, in Want to get rid of ‘rip-off’ degrees, Rishi? Try abolishing tuition fees, by the British columnist, journalist and author Zoe Williams (born 1973), published in The Guardian (London and Manchester, England) of Monday 17^th July 2023:

The concept of the “Mickey Mouse” degree has been long cherished on the right as a way to flag their anti-intellectualism, whereby all learning is useless unless it’s physics, while blowing a class-war dog whistle, whereby all universities except Oxbridge are front operations for the loony left.

The earliest occurrences of the expressions loony left, loony leftism, loony left-wing, loony leftist, loony lefty and loony left-winger that I have found are as follows, in chronological order:

1-: From A Matter of Geography, an editorial published in the Cut Bank Pioneer Press (Cut Bank, Montana, USA) of Friday 4^th May 1945:

Radical group policies sometimes seem to be a matter of geography.
Here in Montana the loony leftists proclaim the present primary law as untouchable. One of their leaders, in a letter to me some time ago, owned up with a commendable frankness that he knew that the primary as now constituted was a destroyer of party responsibility and hoped the day would come when there would be no political organizations in this state.

2-: From It Is Time To Clean House, an editorial published in The Daily Argus (Mount Vernon, New York, USA) of Wednesday 30^th October 1946:

In the person of Thomas E. Dewey we have at Albany an executive of the greatest state of this great Republic who has proved himself the most able Governor of our times. […]
[…]
Nothing throughout the entire Country will so shock and so sadden the looney left-wingers and the parlor pinks as an overwhelming reelection of this proved administrator. Nothing else can inform the hypochondriac New Deal that its time is up and its demise near.

3-: From a letter to the Editor, by one John Daly, published in The Shreveport Times (Shreveport, Louisiana, USA) of Wednesday 7^th April 1954:

Never heard of John Temple Graves until seeing his column in The Shreveport Times. Senator McCarthy is a phobia with John. Too bad!
Doesn’t he realize that the Fifth Amendment unmentionables discredit themselves more than the Senator?
The Looney Left ignores the fact that they are the first to be shot when the Marxists take over.

4-: From a book review, by Siriol Hugh-Jones, published in The Tatler & Bystander (London, England) of Wednesday 28^th September 1960:

A Number Of Things, by Honor Tracy, is a wild, passionately irreverent and enormously unrighteous (according to current In-Attitudes) career round the Caribbean with Henry Lamb, a darling young Candide who becomes involved in any amount of trouble through visiting the locale as the special correspondent of a loony left-wing publication (I can’t think that there are many still in business as loony as all that), and records his impressions as seen through innocent yet profoundly disabused eyes.

5-: From the Lebanon Daily News and The Lebanon Daily Times (Lebanon, Pennsylvania, USA) of Thursday 1^st March 1962 ¹:

Holmes Alexander ²
If JFK Wants To Find Out What’s Wrong With U.S., He Should Look At Loony Left

Washington—President Kennedy is right in observing that foreign students judge (and condemn) America from a stereotype that is “almost 50 years old.” We are suffering from a day-before-yesterday delusion which persists everywhere in the world. But the question is—why?
The reason may be a lot closer to home than the President is willing to believe. Foreigners, with dizzying inconsistency, still think of the USA as being “isolationist,” “imperialistic” and, as a nation, one-third slavocracy, one-third robber baron, one-third oppressed Labor.
If the President wants to know why these misconceptions exist, he should look to the Lunatic Left, which is intellectually mired in only-yesterday (McCarthyism) and the period of day-before-yesterday, which stretched back to the Good Years, as Walter Lord dubs the era between the turn of the century and World War I.

¹ 1^st March 1962, not 1^st March 1961, as erroneously stated by the Oxford English Dictionary (online edition, June 2023).
² Holmes Alexander (1906-1985) was a U.S. historian and journalist.

6-: From a letter to the Editor, by one Stephen H. Trotter, published in the San Francisco Examiner (San Francisco, California, USA) of Thursday 29^th November 1962:

The American taxpayers could be relieved of the crushing burden of the Illfare State by allowing the free market to work its wonders, uninhibited by the whimsical caprices and wild-eyed schemes dredged from the fever swamps of the looney Left.

7-: From The Santa Fe Birdwatcher, by Oliver La Farge, published in The New Mexican (Santa Fe, New Mexico, USA) of Sunday 7^th April 1963:

Altogether too many of us have become conditioned to irrational, purely emotional response to the loony left or the rabid right as the case may be. In last Sunday’s paper, a boy had a letter that defended communist dealings with Cuba and other countries in terms so wildly removed from any possible relation with the facts as to be pathetic. This curious demonstration drove a number of adults wild.
[…]
There is no reason whatsoever to believe that this kid has been exposed either to the loony left or to consciously dishonest communist propaganda. He just seems, homehow [sic], to have been isolated from everything that has been said or discussed, by our side, by Kruschchev [sic] himself, by Castro, in the newspapers, the magazines, including the excellent “Scholastic” publications our school children are encouraged to read, the radio, teevee—everything. It is remarkable.

8-: From a letter to the Editor, published in the Press-Telegram (Long Beach, California, USA) of Tuesday 7^th May 1963:

The Looney left would rather be Red than dead, while the Righteous Right would rather be dead than Red.

9-: From a letter to the Editor, by one Courtland M. Asher, published in The Muncie Star (Muncie, Indiana, USA) of Friday 26^th July 1963:

“Forced” integration brings memories when “Teddy” was our President—what action he would take if alive, and One World Lefties, the J.F.K. clan and constitutional law haters now controlling our government in their attempt to destroy our sacred American Way of Life? The proposed UN-Civil Rights law plus most all deceptive action by JFK clan may get votes for Lefty One Worlders and will backfire. […]
[…]
A modern Looney Lefty One Worlder would have probably issued a [sic] order that Boots stable his team, integrate them with the jackass under Civil Rights ‘Law of the Land’. Our “Teddy” in 1906 would have used the Big Stick and One World Loony Leftists would have brayed mournfully in retreat. We need a “Teddy” to pilot our ship of state.

10-: From The Dove May Be A Decoy, an editorial published in the Alabama Journal (Montgomery, Alabama, USA) of Thursday 17^th October 1963:

AFTER THE LIMITED test ban treaty and the wheat deal with Russia, anyone who stuck his head up and warned Americans to continue to regard every Soviet move with suspicion invited attack from the loony left.
Don’t rock the ark of peace just as it appeared under way, the pale pacifists were prepared to say.