This question is difficult to answer without having precise details of your insurance policy and the terms you signed-up for.
There are certainly occasions where some insurers might consider that a holiday was booked starting in Ireland and therefore not within their limit of cover.
This was a recent example of someone who was not covered as AXA said her trip to South Africa had started in Kenya and not the UK.
The point is really that you just need to check the specifics in your case.