Trains in the rush hour in the UK are pretty much always full, with people standing up. The tube at rush hour looks like this:
https://static.standard.co.uk/s3fs-public/thumbnails/image/2...
If it's not too expensive or infrequent I imagine it will be very popular.
Especially given the picture you provide, I think you're talking about intra-urban rail (subway, metro, even suburban commuter).
That's a far cry from a 350-mile, 3-hour inter-city link.
Show me the picture for the London-Edinburgh "rush hour".
Southend to Liverpool is 3-4 hours on the train.
That's only, what, 240 miles? Which means it's not exactly high speed, is it? It could probably reach the 25k/hr that my sibling commentor is asking for, but not the 100k claimed for HSR.
Additionally, if it's Southend-on-Sea, that's not a major urban area. At 25k/hr, you could move the entire population to Liverpool in a little over 7 hours. I smell a contrivance.
Lastly, the name of that picture describes the train carriage as "busy" not something like "typical", so even then I'm skeptical.
Try again. London to Edinburgh. High speed. Typical rush hour.
I'd say 4x that amount for a full-sized HSR train is credible. It's just that that's a maximum. I don't believe that ridership will ever be high enough to approach that number, unless air travel is outlawed.