From Longman Dictionary of Contemporary Englishset your face against somethingset your face against somethingespecially British EnglishAGAINST/OPPOSE to be very determined that something should not happen The local Labour Party has set its face against the scheme. → face
Examples from the Corpus
set your face against something• Alternatively, the rule-makers can set their faces against the pressures for change.• The Lord Chancellor set his face against growing criticism over his behaviour.• It has set its face against cutting prices.• Does the hon. Gentleman really want to set his face against the improvements that trust status could deliver?• I would set my face against the casualisation of the Corporation. 