The person has been identified as Jac Holmes.
He had been fighting with Kurdish militia the YPG since 2015, media reports said.
Kurdish representatives in the UK said they had been told by YPG officials the former IT worker from Bournemouth was killed while he was clearing an area to make it safe for civilians, BBC reported.
His mother, Angie Blannin, told the British news channel: "He loved what he was doing there, he loved being a soldier. He had the courage of his convictions."
"He was just a boy when he left the UK, a little bit lost. He told me he didn't know what he wanted to do with his life. But by going out there, he found something that he was good at and that he loved," she said.
She said she has not seen her son for more than a year.
"We thought with any luck he'd be home for Christmas. It had been so tough since he had been away but I was always 100% behind him," she said.
"After all this, he had said he might go into politics, or perhaps into close protection security. He'd seen so much for a boy of his age," the mother said.
Ozkan Ozdil, who also fought with Mr Holmes in Syria, told the BBC his friend had become well-known and respected among Kurdish fighting units.
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