This plan has been in the pipes for ages I think. Someone posted on here exactly how it would be almost impossible to do, possibly something about the depth or state of the bed of water , can't remember.
Wasn't this debunked last year due to the massive munitions dump off the coast of Scotland ?
Yup, here's what
I scribbled last year (which took fucking ages to find as Google wasn't playing, in the end checked out the date Boris last mentioned this and looked at my posts from around then):
Yeah, this was all ripped apart the last time he mentioned it. As has been said, this is just a distraction tactics from the news about the court ruling and Cummings' attempted data-snatch.
For the reasons that have been stated, the shortest route is completely impossible due to depth and
Beaufort's Dyke (super-deep and full of explosives).
Having done it myself via ferry it really is amazing how short it is, but unfortunately the journey to get to that bit of Scotland is non-trivial (two hours plus by train & coach from Glasgow alone) so unless they also opened a high-speed road/railway to get there it'd be largely pointless anyway.
There are a couple of other routes but ultimately the only one that would make any economic sense at all would be Holyhead to Dublin... which is also the longest, thus unlikely to happen. Would probably work best as a tunnel... still staggeringly deep though but the Japanese have apparently gone deeper.
The other issue is that Irish trains (such as they are) run to an entirely different gauge (5'3" instead of 4'8.5"), so through-running would be extremely difficult.
I'm sure I read about all this on a Railforums thread a couple of years ago, but the only one I can find now is this much older one (which links to older ones still), but it repeats many of the same arguments I remember reading before:
https://www.railforums.co.uk/threads/united-kingdom-ireland-tunnel.77694/

(Click to expand this one.)
I think tunnels further south (e.g. Holyhead to Dublin, or maybe Whitehaven/Barrow-in-Furness - Isle of Man - County Down) are probably the only viable option.