These two stanzas were suggested in the first place by an actual incident. Mr Johnson’s main advisor Dominic Cummings was making himself surprisingly available for stray encounters around Westminster. See here, for instance : https://www.facebook.com/watch/?v=752395791889320
The reference to Cox in the second stanza is to Geoffrey Cox, the Tory Party’s Attorney General. He performed theatrically in the House of Commons, following the re-call of Parliament, helping to drown out the true implications of the Supreme Court’s recent decision (and presumably its judgement on his earlier advice to the government that prorogation would pass muster), by raising his voice and shouting “chicken” at the Labour MP’s opposite.