It's interesting that high speed rail comes up for discussion as the UK is leaving the EU. A cross border route between two member states would qualify for EU funding. A cross border route to a non-EU country wouldn't, though I'm sure some funding could be wrangled under the heading of "peace process".
Has anyone even thought about whether this would be a new route, or upgrading the existing lines? Upgrading would have the advantage that other services could take advantage of the higher speed tracks, and would probably be less costly, but would have the downside that high speed could get stuck behind slower service, delays could arise.
The rollout of high speed lines in Spain would be worth analysing. Some of their lines have quite low population density, and it's hard to see them ever being viable without massive government subsidy.