Home guard and Armour?

[Steel God]

When you say “tank” you assume you mean fully tracked vehicles and not armored cars, in which case the Home Guard never had any (nor would they have reason to have had them).

British armored formations in 40-41 would have been variously equipped.  The RTRs would have had infantry support tanks, Matildas in 40 and into 41 with Valentines replacing them in 41.

The armored brigades would have had Cruiser models in 40.  They would have remained in service through 41 but begun to be phased out and replaced with Crusaders in 41.  In 41 you also had large numbers of American lend lease M3 Stuart’s being fielded.