Christine Blower, NUT general secretary, told BBC Radio 4's Today programme it was "a little disappointing" Mr Gove had written to Ofqual "without having had this discussion with the profession".
She said: "There is a lot to commend A-levels, but there is no harm done in having a look at them again.
"What we don't want is to have proposals put to us on a take it or leave it basis."
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Host Paddy McGuinness tweeted a tribute to contestant Charlie Watkins whose date was featured in Saturday's episode.
A police raid uncovered what is believed to be cocaine that had been stashed in nappies, and 40 cannabis plants.
The prince attended the rugby match in his role as patron of the Invictus Games Foundation, the official charity for this year's game.