I am from England and happen to personally know many people close to Rabbi Mirvis and have personally met him a few times. On every shaila in halocha, such as this one, he refers to the London Beis Din, all of whom are outstanding talmidei chachomim, each of whom i have spoken to on several occasions. In response to one of the above points about entering a beis avoda zara, the proof from Chana and her seven sons is not followed lehalacha, except in a שעת השמד, see Y.D. 157:3. The current reality in the uk is not a שעת השמד. It seems that this was also the psak of Botei din in London in the past