"Barack Obama was probably not aware that he was doing anything unusual when making a toast 'to the Queen' and then continuing with a short speech."

BBC explains:

According to protocol, however, he should have stopped after the toast.

The band, taking its cue from the word Queen, struck up with the national anthem leaving the president struggling to make himself heard.

What happens when the Queen is toasted is all part of protocol, an elaborate set of customs and rules that govern interactions with the British royal family....

[I]t stems from a time when monarchs were accorded an almost divine status and had to be treated accordingly....

Whatever the original or the details, the President intended and wanted to follow the protocol, and somebody on his staff did him a grave disservice by not making absolutely certain he was getting it right.