I just cannot see how the economics would work, the Channel Tunnel cost around £20 billion at todays prices, and would probably cost twice that if construction was in progress now. An Anglo Irish fixed link over a practical (ruling out any route across the North Channel) route is roughly twice the distance, so that puts construction costs in the 60 - 80 billion range, possibly even a lot more. Then add a significant amount more for infrastructure at either end. To put it in perpective thats around £1000 for every man woman and child in the UK and Ireland. I just dont see how it could be funded. The Channel Tunnel has had a rocky ride at times financially, and thats nowhere near the cost of an Anglo Irish fixed link.
I think there would serious public disquiet about the hike in taxes that would be required to pay for it, some quick sums would indicate maybe 3p on income tax for 10 years as the sort of ball park impact, which means political suicide for any government proposing the idea.