Rolling with it is much easier if you have money. And not travelling with kids.
My biggest travel disruption was when I was trying to get from London to Brussels and all Eurostar services were cancelled due to a body on the line. It was absolute chaos at St Pancras and people were waiting around to see when trains would resume.
I knew I would not be able to cope with the stress and queues. Luckily I was travelling alone and at the time I had disposable income so I found a corner and some wifi and booked a flight to Brussels later that day. It cost a lot more due to late booking but we’re talking maybe £300 I think (a lot for a flight to Brussels but not a bad price to avoid the stress).
I then put my suitcase into storage and enjoyed my extra day in London.
My instincts were right, as in fact all trains were cancelled until much later in the evening, and we were offered refunds if we wanted to cancel.
When I returned to St P hours later to pick up my suitcase and get the tube out to Heathrow, it was still stressful and chaotic. I felt very Zen as I got in my flight.
But the key was: I was alone, I had a certain amount of money to fix the problem, I didn’t have children with me.