But if the foreigner controls the company, it may have a presence in the UK
Hypothetically, even if a "presence" subsists in the UK it would need to be a "p/e" and in addition trade would need to be carried on through it for a corporate tax exposure to arise and hence a requirement to report.
If either condition is not satisfied then even if there is a UK "presence" the non-resident company must be trading in the UK to precipitate an income tax charge and hence a reporting requirement.
Under either scenario it is the company not the "foreigner" referred to by the poster who has the obligation to report.
The foreigner will only have an obligation to report income of the non-resident company if he/she falls foul of an anti-avoidance provision (eg s 735) which is unlikely (although possible) if non-UK domiciled.
Bottom line is that the query is far too general for any reasoned response to be provided.