> Hum, there are a lot of trains from London to Manchester today for between 42-47£. Those do take 3h45m.

Those are indirect train services. That can also be the return price, which is very very good value. You do have to be careful with travelling the right route and company

Yes. I didn't see the slow trains, it looks like they were hidden from my search.

(Also bear in mind the median income after tax is 50% higher in Denmark.)

> it looks like they were hidden from my search

I don't blame you. They do make it VERY hard to find and buy that particular cheaper ticket

Ticket websites generally assume you have unlimited funds and want the fastest route, always.