I am sorry but UK mortgage companies can refuse mortgages if you are unable to effect a life insurance policy...It is up to the individual lender.
What would make your case less of a risk is the following..
1. Low Loan to Value , ie you borrow as litle as possible and use up your cash from the sale to purchase your new home, this is less risky for them.
2. Have you a partner ? Are they working ? Because if anything should happen to you could your partner continue paying the mortgage without difficulty ? Then they would be happy to waive your life cover !
3. Apply for Uk Life insurance now, while you have no real Life issues.
4. Have you a pension with Death in Service attached in your new job, although they cannot assign these policies they like to know that they are in the background.
5. If no one suffers in the event of ....., ie that the bank is not kicking out someone so that they can sell the house, then they may also waive your life cover as the house can be sold, without making someone homeless.
6. Can you keep your irish policy going, ask your insurance company here about you leaving ireland and the implications of same, you will then need proof for the uk bank that all your premuims are up to date at the time of applying for the mortgage.
Good Luck