Both 1st Northamptonshire Yeomanry and 51st HD were attached to the 1st Canadian Army (II Canadian Corps) for the latter part of the Normandy campaign. So for example, the left hand column of Operation Totalise on the night of 8 Aug 44 consisted of 1NY (from 33rd Armoured Brigade) and 51st HD from 154th Infantry brigade supported by specialised armour from 79 AD (XXII Dragoons - flail and AVRE from 1st Assault brigade RE). One company of 51 HD was carried in SP gun chassis converted to APCs - these belonging to the 25th Canadian Armoured Delivery Sqn. This column was under Canadian command - as was the 1st Polish AD which took part in the follow up actions to the night column action. Hence the debate about who eventually killed Wittmann. Best evidence is Trooper Atkins in a Sherman Firefly belonging to 1NY (if you believe Ken Tout who has wriitten extensively about the campaign and was also in 1NY).