I had the good fortune to stumble on this place whilst out in London with a friend. I didn’t ask them about whether they had a policy on playing music, however when we were there there wasn’t any, or at least it was so low that you couldn’t really hear it.
The restaurant does a nice range of standard Italian fare, with a range of pizzas and vegetarian options. Not particularly expensive, a good alternative to pizza hut\pizza express etc.
London W1S 4JF