Why should it put any pressure on the UK government at all? They are not the instigators of any plan by CHC to shuffle their own aircraft about as they see the need for their other contracts. The UK customer will be entirely (and only) concerned about CHC meeting the specific requirements and transition schedule of the SAR-H contract and its timings (which are probably (in reality) slipping as we write.
If CHC have taken a risk in offering the Irish some ac that are coming off another contract, then the Irish customer should have sussed this and have either accepted some potential delay, or will no doubt be getting upset soon with CHC if they fail to deliver in accordance with the Irish contract.
That all said, I have little doubt that CHC will be lobbying the UK customer to get on with its decision to minimise its potential exposure with the Irish.