It happened a couple of times in the 2016/17 season.

On 15/10/16, Bournemouth beat Hull 6-1. All five of their goalscorers were English (Junior Stanislas scored twice).

A few weeks earlier, 18/09/16, Crystal Palace had beaten Stoke 4-1 with four different British goalscorers.

I don't think it happened at all last season, but I might be wrong.