Not to mention that it's money "earned" on her private property, that the government manages on her behalf.
If I had a second house (I wish), and rented it out through an agent, then claiming the sovereign grant is "taxpayer's money" would be like claiming that rent is the agent's money, they're giving me as a gift.
The queen owns lots and lots pf properties, all over the country (and outside). She gets rents and earnings directly from the Duchey of Lancaster; the rest is as above (managed by the government, and handed over to her)
IIRC though, the taxpayer does top it up if the money earned on the royal estates decreases year on year - so this year specifically, there may have been an input from the taxpayer.
Having said all that - I'd be all in favour of shrinking the royal family to a more nuclear family; and mostly in favour of getting rid altogether.