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His early writing career included some involvement with Unity Theatre, London, where he contributed material to a number of revues.
His poetry featured regularly in Radio Times and other periodicals in the 1970s. During much of the 1980s and early '90s, he had his own weekly poem in the humour magazine Punch: titled "Subverse". This consisted each week of a humorously subversive political poem, often dealing with recent events. He was also New Statesman's weekly poet from 1970 until months before his death, following in the footsteps of 'Macflecknoe'; 'Sagittarius' (Olga Katzin); and Reginald Reynolds; and succeeded by Bill Greenwell.
His poems featured topics such as the Vietnam war, miners strikes, and apartheid.
He also wrote for television, including an episode of The Prisoner ("Hammer into Anvil", 1967) which is generally considered the most literate episode of that highly literate series: several pieces of classical music figure in the plot; one character quotes Goethe in the original German, and another character quotes from Don Quixote in the original Spanish.
Much of Woddis's writing was openly sympathetic to leftist political causes, including communism. Woddis's obituary in The Times confirmed that he had been a member of the Communist Party of Great Britain.
His poems include Ethics for Everyman and Down with Fanatics. His collections include 'Lot 71' (1971), 'Sex Guyed' (with Arthur Horner, 1973), 'The Woddis Collection' (1978), 'God's Worried' (1983), 'Funny Old World' (with Steve Bell, 1991), and the posthumous 'One Over The Eighties' (1994)