Not really my thing either Peter as I'm always confused by Regiments etc. but I'll have a stab in the Cassino-related absence of two leading 'Regimentalists'.
6/7/44 they joined the 49th Division
British Light Infantry Regiments & National Service
As part of the 147th Infantry Brigade.
And it seems from this site on the Leicestershires they spent 1944 heading towards Le Havre and crossing the Seine, after breaking out from Cagny once the Caen fighting was done:
Green Tigers - Normandy.
They happen to be the town Battalion for Leicester and I'm often in the vicinity of their Regimental Museum, and the local records office where the war diaries are apparently kept so if there's anything more specific needs looking into I can easily ask there.
Cheers,
Adam.