Isn't this basically Pickett's Charge at Gettysburg?
Advance troops for about a mile over open ground vs rifled muskets (many of which were indeed P53s)?
Might be interesting to look at significant repeating rifle vs P53 engagements in the US civil war. IIRC Spencer rifles were used in quantity by infantry units at the battles of Chickamauga and Nashville.
The major difference with the US civil war is the level of training though, which is why many engagements were typically fought with rifle muskets at smoothbore ranges. When your first shot is fired live in actual combat, there's no way to train troops to the level of marksmanship that the British Army was trained to, rendering them capable of delivering fire at substantial ranges (as show in the Crimea and in India). This changes the calculus with respect to any US civil war comparison somewhat.