Wild Honey in Mayfair is lovely, classic and safe... great food and atmosphere. https://www.wildhoneyrestaurant.co.uk/
Also, I'm desperate to check out HIDE. The chef is Ollie Dabbous and I went to his earlier restaurant "Dabbous" which was amazing. He uses local, organic products in simple yet hugely exciting dishes. I haven't been to HIDE but if it is anything like Dabbous, it will be amazing! http://www.hide.co.uk/ollie
Also, not central but Chez Bruce in Wandsworth is always a winner!