You have to remember that this is a leaked statement.
The queen isn’t aloud to take public positions on political issues, but she has a weekly meeting with the Prime Minister in which she can air such statements.
I fully suspect she may have a very dim view of Islam. I’ll bet Churchill advised her early on that.
So why have her around? I've never understood why the Brits still have a "Royal Family" when all they do is piss through money.