Plan B if there are track or signal issues?

trains from Leeds to London run down the same east coast line as trains from York. So you'd likely have to go from York to Manchester and take the train from there, down the west coast line. Or a train from Sheffield to London would be possible.

or there's National Express coaches, Megabus, maybe Flixbus to London.

Make sure you have travel insurance.

There is very little coach service from York to London, by any operator. There is a frequent service from Leeds.

To add to your potential woes yesterday afternoon the entire Piccadilly line was closed to Heathrow for several hours due to a major signal failure at Wood Green, miles away. The Elizabeth Line was packed out. I was caught up in the mess.
In that case I used one of my tried and tested stand by routes- bus/train via Feltham to Waterloo.

And on Monday elsewhere I got caught in a major track incident causing a near 5 hour delay.

That is why we always say to stay in your departure city the night before.

Today LNER arrangements have ticket acceptance via Sheffield. Via Manchester a new ticket would be needed.

"That is why we always say to stay in your departure city the night before."

This is a key point from Stuart. I would not try to make this trip on the day of travel.

One time coming from York to King's Cross my train was delayed by an hour because it hit an animal on the tracks north of York. Then there was signaling issues and we sat on the track for at least an hour as 2 other train loads of passengers piled onto our train. I was seated but many had to stand all the way to London. Every other time I've done this journey it's been fine but every now and then there can be a failure.

Lower your stress level and go to London/Windsor/Heathrow the day before.

By the way last night there were apparently two major incidents on the M1 motorway.
At one stage the story I heard was of 15 miles of standing traffic. My bus driver from London to Leeds (for York) was expecting a 2 to 3 hour delay so diverted via the A1/A52 omitting stops. I've had a bit of a week this week.
At last I am relaxing on a Leeds to Carlisle train.

now today a world wide IT failure is cancelling flights and trains.

Stuff happens. No way I would be half way across the country the day I had to catch a flight home, even if it was in the evening.

I'd want to be nearby.

To be constructive, if you can't change your last night's hotel- you can take a direct National Express bus twice a day from Leeds to Heathrow (all terminals) via Luton Airport at 0015, arrive T5 at 0740 (T2/3 and T4 a bit earlier), and at 0645 arrive 1420. There is a 24 hour a day York to Leeds train service, so York to Heathrow is theoretically possible by bus.

If you had to York to Leeds is about 17 miles so something like a £40 taxi ride.

Northbound, for the record, services leave at 0850 and 1550.

Other bus connections are possible through Central London broadly hourly from Leeds.

Here the OP already has things booked, so it's looking for a plan B, C or even Z. It's also worth saying that all ticket restrictions in such events get lifted, so if, say, a 10am train was booked, but there are big problems early on, my instinct would be get to York Station ASAP and get the first train south, travelling hopefully.

Then I idly wondered as to whether there actually was a bus direct from Leeds to Heathrow. You never know what unlikely routes Nat Ex have half the time. So, to try to be helpful, I looked it up on the off chance.

I've not checked whether Flix bus or Megabus have one.

Let's face it you'd have to be up really, really early in York to catch the direct day bus. Given how long it takes the bus to go from Leeds to London there is room for debate on whether via London is a viable route.

While I'm on the train I am then going to be googling, what on earth do I do if the train gets terminated short of London. But with a theory that the closer to London I can get the more options I should have,

You can change your plans if they aren’t going to be workable or if they’re too risky. There are other trains, other hotels. There are other flights too but the cost of missing a flight is far more significant than the cost of a new train ticket.

I would not want to travel from York to Heathrow on the day of a flight and I would not recommend it to any other traveller either.

The usual way to make a long journey like this avoiding an overnight stay at Heathrow is to book a connecting flight from say Newcastle then any delay is on the airline not you.

Two years ago when there were several national rail strikes as a backup plan we booked bus travel on National Express. The route went from York to Leeds and then onto London, and there were several per day but they take 6-10 hours total. In the end the trains ran the day we needed them so didn't take the bus. I agree with everyone else advising against doing this trip the day of your flight.

Ok, wow, thank you all.
While my original question was specifically about ‘what if there are transportation system issues shortly before or while in transit while going by train from York to Heathrow the day of our flight’, I am grateful for all the detailed responses on how to react and reroute that day. That’s the info I was looking for, and hopefully won’t need.

As a bonus, you all provided excellent real world examples of why the trying to get across the country the day of the flight is definitely a flawed plan. Yikes, what was I thinking?!?

(Well, what I was thinking was that the 3 hour train York to London is comparable to the 3 hour drive to SeaTac or 4 hours by train. And if there are problems there are several alternative routes and modes to make that journey. Heck, I know people who have left early to get to the Seattle passport office for same day processing and still make their evening flight.)

But really York to London is more comparable with trying to get from San Francisco to LA for a same-day flight. Sure you might be able to drive all that way, but any number of things could delay your journey and miss your flight.

So we have changed our plan and are actually happier with it. The visit to York was for less than 2 days. So we have canceled that (train tix and lodging both refundable). And can stay another day near Hadrian’s Wall, adjacent to the Dark Sky area. Which allows us to stay up late to watch the Perseid Meteor showers as they approach their peak.

Then we travel in the afternoon the day before our flight, and stay at the Hilton Garden Inn at Hatton Cross, just 2 Tube stops from T5.

Thanks again for the sage advice!

Now who can I ask about skipping the next software patch?

Every cloud has a silver lining as they say, although clouds are the last thing you want if hoping to see the Perseid shower!!