First off, I assume the "State Secretary" is an elected politician, not an official (civil servant)?

A politician's legitimacy is provided by the electoral vote. In matters of national security, the UK does perform background security checks on its ministers (politicians in charge of a government department/govt business), as on it's officials.

Banning multiple passports sounds rather like not trusting people simply becasue you perceive them as foreign. There have been plenty enough traitors who are not "foreign" to a given state.