It's a bad argument to compare the prices for one service in two distinct countries and then imply that the price difference must be due to regulation. There are a lot of other factors going into the price difference - from fuel prices, car prices, repairs, to taxes and other differentiating factors. Prices also always relate to the average cost of living in the area.
The average earning per km in Berlin is somewhere around or below 1,50 EUR before costs (anecdotal evidences but from a credible source). Nobody really gets rich from that - not even the cab company.
I don't think you realize how small a kilometer is! Or how valuable a Euro is (in terms of real money like dollars). That sounds to me like an incredible rate of profit.
These cities in the UK that cost three pounds to cross half of. Are they some kind of special, tiny city? Perhaps made out of lego? An awful lot of taxis charge a couple of quid as the minimum fare just to get in it, so where you're getting these taxis I don't know.
Here's a big list. Even allowing for the inherent unreliability of the internet (and some of those prices look a bit suspicious), just which city is it that costs three pounds to cross in a taxi?
Those prices look suspicious indeed. Most of my experience is from Glasgow around 2010.
I just entered a journey I made often (home in north-west Glasgow to the central station) and that website came up with £13.50. I clearly remember paying £5 with tip for that journey from a local taxi company.
Even with the dominant black cab company, I don't remember going home from the city centre late night for as much as that.
In Paisley, which is a bit smaller, I took taxis to the airport for £3 or £4.
The average earning per km in Berlin is somewhere around or below 1,50 EUR before costs (anecdotal evidences but from a credible source). Nobody really gets rich from that - not even the cab company.