I don’t know if I’m not a Talmid Chocom like Chief Shemerel (I guess that is why he is a Chief and I’m just Smerel) but he seems correct. As far as I know the policy of the Chief Rabbi and London Beth Din is to enter a church only if the Queen (now king) commands. Invitations to coronations, royal weddings and funerals have the status of such royal commands.
Rabbi Sacks was not the first British chief rabbi to attend such events. When asked why he did so he said:
“For at least 150 years, British chief rabbis have attended such functions. In America you don’t have something like this. In Britain – because we have a queen and an established church – when there is a state occasion, the Jewish community is represented by its religious head. That is a civic act, not a religious act. Every chief rabbi has always attended a national service, even if it was in a church, as a civic representative of the Jewish community loyal to the head of state. This falls under the halachic categories of mipnei darchei shalom and mipnei eivah. ”
Of course there are exceptions and rules Rabbi Saks himself did not attend Diana’s funeral because it was on Shabbos (not because it was in a church) and his predecessor did not attend the church part of the Charles-Diana wedding (it was enough of a ceremony for him to find other places and time to show up)
There are plenty of boich svoras I can say and “rayos” I can bring either way so I’ll stop here and say that it isn’t so simple. Different poskim will rule differently on what is Pikuach Nefesh for Yom Kipper and Shabbos. So too for this question. Those who believes that participation in government ceremonies when they are expecting you to is a form of communal life-saving activity have what to rely on . I was told by semi reliable sources that Rav Shlomo Zalman Aurbach told that to Israeli diplomats . I was also told by semi reliable sources that the mayors of Lakewood NJ got a hetter from the Lakewood poskim to attend the funerals of Lakewood policemen killed in the line of duty in Lakewood even thought those funeral took place in a church (don’t know if either of them are true)