Not only is the Queen of German ancestry, I believe I am right in saying that her mother would probably be classed (before marrying into the British royal family) as Scottish.
"Jerusalem" would be the most preferable of the established suggestions. However, a new song would be even better.
That wouldn't mean that the Scots would respect a new English national anthem, any more than "God Save the Queen". They will continue to carry a negative attitude towards our country and people, and maybe only political change will alter that.