Thank you, KGarrad, we know of the well known Betty's - it would have been so much easier if it had been that tearoom. But my husband is pretty confident it was Mimi's she spoke of, with a mention of Gillygate. Google Streetview shows a number of cafes & tearooms in Gillygate & one called Evie Brown's Tearooms in Bootham right opposite Gillygate. I had hoped someone local might remember one called Mimi's, even if it was at least 30 years ago.