London-Birmingham is so cheap because of real competition between different franchised operators! That's just something we don't get in Germany. The various TOCs operating regional trains usually have to follow the Verbunds-/Landestarif and the only respectable player for long-distance trains is DB Fernverkehr, wholly owned by DB AG, wholly owned by our "competent" nation.
A slightly more intresting route might be Köln-Hamburg, about 355km (as the corw flies):
Flixtrain offers Advance singles from 9.99€, looking for 12th March (11.01 ex Köln), I get a price of 14,99€.
DB offers tickets from 19.90€, looking for 12th March, I get a price of 29.90€ for the 11.09 IC or 19.90€ when using ICEs via Hannover, Flexpreis at 93€ or 103€ respectively.
Now consider that you can get 25% off with a Bahncard (staring at 19.90€ for 3 months or 10€ for five years for anyone under 18 - dirt cheap!) but also - quite importantly - realise, that Flix only offers one or two trains per day on it's routes, in this case meaning that you will have to travel on the 11.01 ex Köln whilst DB offers loads of trains all day long. If the Flix is cancelled, you will need to get yourself a ticket for DB and get it paid back, which (rather unsuprisingly) is quite complicated.
Let's look at London-Birmingham again: There are three TOCs offering very frequent services, with slightly different journey times and stations (Chiltern). Due to this, they have to offer either a better service (I think of Chiltern's Mk3 sets with their very decent legroom) or very cheap prices: Virgin starts at £5, Chiltern at £5.50 and WMR at £7. I can not comment on the aviabillity of these fares, but that is very cheap. If your train is cancelled, you still have enough other options your ticket will be valid on (even obeying operator restrictions). It's pretty much the same on flexible tickets, but the WMR ones are slightly cheaper.
The big plus is that the British network has off-peak walkup tickets, so that you can still take any train you want for a smaller price and a slight restriciton in valdility. In Germany (on Fernverkehr tickets), this only exists by weekday (Monday and Friday should be the most expensive days and Tuesday and Wednesday the cheapest), makin off-peak flexible travel quite expensive. I can only remember travelling on a Flexpreis once and that was for Köln-Duisburg, where it was cheaper than a Sparpreis (at short notice for the goods line from Köln to Duisburg).