I am a British citizen and a revert to Islam. All my three children and I have British passports. My husband is planning to make the Hijrah with us to his homeland in Morocco. He himself is planning to drive back and forth to Britain for business purposes only buying and selling trade. Without a British passport he must always have to apply for visas. Is it permissible for him to apply for a British passport for traveling purposes only, bearing in mind that to do this he must pledge allegiance to the Queen?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Taking the nationality of any non-Muslim country for the purpose of business or comfortable life is not permissible. There are many legal prohibitions in this practice such as taking the pledge of allegiance, exposing oneself for the temptation, etc.
A person may trade in Muslim countries; one should prefer the countries that observes the religion, the forms of worship, the good values, and the good conduct.
Allah Says (interpretation of meaning): {… And whosoever fears Allâh and keeps his duty to Him, He will make a way for him to get out (from every difficulty). And He will provide him from (sources) he never could imagine …} [65: 2-3].
Therefore, your husband should avoid taking the nationality of a non-Muslim country. For more details, please read the Fatwa: 82552.
Allah knows best.