As a regular used of "Addy Lee", I've found that's not normally true if you go for the standard cards (the Ford Galaxy): from my home to Euston is about £20 in an Uber, £35 in a black cab, and about £25 in an AL.
Given Addison Lee is not VC subsidised, you have to wonder how they're getting the price down, but I always choose AL when I can.