What is the name of the red chili pepper that the English chefs use?

Ottolenghi does the same. All chilis are not equal and we use names to distinguish them in the US because of the variety available. Are they hot? Mild? Sweet? I wish someone would answer this! Red pepper flakes would not be a substitute for the taste of a fresh chili, IMHO.

Interesting question.
I've cooked many recipes from both those writers, and don't remember them ever specifying.
Also, a view of foodstuffs available on Amazon UK indicates may varieties of red pepper, so that doesn't narrow it down or help much.
I've generally used standard red pepper flakes with success and sometimes replaced them with something fancier like ancho, aleppo or marash peppers.
You could use any low to medium heat dried-and-ground chile pepper when cooking for guests or those whose heat preferences you don't know.
Or use a medium to higher heat one for yourself or your household if you all like and can tolerate more heat.