CRA only care about tax residents of Canada, they don't give a dot about your status elsewhere. HRMC and CRA communicate, but only if necessary.

If you have paid tax elsewhere you produce a certificate of tax paid. If you cannot produce that, you have to prove to CRA tax has been paid elsewhere and to whom. If you cannot, you get dinged the full amount in Canada. As a rule, they only know what you tell them, or someone dobs you in. Once an audit starts (you don't want that), there is no tellings what digging around they will do, up to 6 years back, longer in some cases.