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When can I re-apply for the UK Visa after OVERSTAYING for 2 months?

I have applied twice for tourist visa but got refusals. Second time I received a letter saying "when I was still in the UK I should have received a notification about my overstay" (I never did) and HO were not sure if I would leave the UK after my visitor visa expires this time. When can I apply for other Visa again? Should it be 1 year after I came back to my home country?