While it looks like the orchestra stepped on Obama speech, the problem was that Obama jumped the gun on the orchestra who were supposed to go first. You will notice that the queen does not touch her glass until after the anthem with Obama apparently realizing something is wrong putting down his glass when he realize he is the only one holding one.
Video embedded below.
"Protocol, apparently, requires the toastmaster to wait until after “God Save the Queen” plays and then begin the toast. But the almighty O waits for no sovereign, so he launched straight into his shpiel. To which I say, good for him. What else was the American revolution about, if not the right of the president to half-ass some formulaic niceties about the British monarch? He should have punctuated it with a weary “whatever” and downed the glass in one gulp."