Read Rav Mirvis’s history regarding “interfaith” and especially his contacts with imams and mosques before you get excited. Lord Sacks raised the stature of Judaism in the eyes of the goyim, and he knew to back down after he took a false intellectual premise related to “interfaith” and inadvertently ended up swimming in the cesspool of kfira. He was far from perfect, but most of the time he created only kiddush Hashem. Same for Lord Jacobowitz AH, especially during the time of Margaret Thatcher, who looked to him rather than to notzri clergy for moral leadership.
Today, with the Muslim mafia in control of most of Londonistan, Khan Manchester and many other parts of the United Caliphate, it is impossible for someone in this position to avoid “interfaith” unless he’d rather face death threats.
This is a “rav mi-taam” position in any case, and as Gatesheader points out, it is immaterial for the Torah-true world. The dayanim of the London Beis Din tend to be reliable talmidei chachomim (I do not know if Rav Ehrentreu is still the av beis din), and they are quite independent of the “Chief Rabbi.”