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I do not think that this is at all likely however with a series of PODs it might just have been possible.
1) No Falklands war
2) Owen gets to lead the SDP and manages to smash the alliance with the Liberal Party (unlikely but not quite impossible)
3) Livingstone's efforts on reducing fares and increasing rates (property taxes) are not blocked by the Courts.
4) Thatcher decides to push through both the abolition of the GLC and the Poll Tax without a specific mandate.
5) Kenny Everett's absurd comments happen at worse time for tories- say and 1983 conference. Remember he got cheers for saying 'let bomb Russia' and "let's kick Michael Foot's stick away". Foot suffers a fall which disables him enough to prevent him carrying on as leader.
6) Livingstone wins a by election and the Labour leadership.
The General election in May 1984 goes something like
Labour 38% 341
Tories 37% 270 seats
SDP (Owen worshipers) 8% 2 Seats
Liberal Party 12% 11 seats
Others 5% 26 seats (mostly Northern Irish)
Labour getting an overall majority on such a low vote and low lead over the tories may sound unlikely but there was already and bias to Labour against the tories in constituences and turn out even then.
What happens next?
Would there be less than Constitutional attempts to undermine the government by elements in the UK.
Would Reagan be tempted to treat Britain like Chile or Honduras?