Question: Does one say the special beracha on seeing the Queen?
Answer: The Gemara (Berachos 9b; 19b; 58a) writes that if one has the opportunity to see a king, one must make an effort to do so (See Shulchan Aruch OC 224:9). Upon seeing him, one says ברוך ... שנתן מכבודו לבשר ודם, Blessed are You… Who has given from His own glory to people. The Mishna Berura (224:13) writes that one should even interrupt learning Torah to see the king if they are accompanied by a royal procession.
R’ Shmuel Wosner (Shevet Halevi 1:35) and R’ Moshe Sternbuch (Teshuvos Vehanhagos 2:139) write that this applies equally to a Queen.
R’ Ovadia Yosef (Yechave Daas 2:28; Yabia Omer 8:22:25) quotes various poskim who say that one only says the beracha if the head of state has the power to execute or pardon (from the death penalty). If they don’t, then one recites the beracha without saying Hashem’s name. Additionally, the monarch needs to be wearing royal clothes. Thus, he relates that when President Nixon came to Eretz Yisrael, they recited the beracha without Hashem’s name as the President was wearing normal clothes (See Be’er Moshe 2:9; Minchas Elazar 5:7:3; Piskei Teshuvos 224:6).
R’ Shmuel Wosner (ibid) and R’ Moshe Sternbuch (ibid), however, write that the honour shown counts more than the power they may have. Thus, one wouldn’t say the beracha upon seeing the US President as they are voted in and out of office every few years. The Queen of England, however, receives much more honour as a monarch, and is responsible for signing every law. R’ Sternbuch relates that R’ Yosef Chaim Sonnenfeld once had a private audience with the King of Jordan and he recited the beracha. Thus, one says the beracha even when the monarch isn’t accompanied by such an entourage.In conclusion, the minhag in the UK has always been to recite the beracha complete with Hashem’s name upon seeing the Queen.