Thanks for the link Allira, when I used the word directly- I meant a government could not directly deprivet without following due process.
Yes a Home Secretary can in certain proscribed circumstances, "directly' deport as set out in your link for certain circumstances and it also sets out the process. Mr Fattah would still have grounds for appeal, as set out in your link:
"People can also be stripped of their citizenship by the Home Secretary but do" have a right of appeal, although intelligence evidence may be withheld. The Home Secretary is usually required to give the person written notice. Notice can be withheld in certain circumstances, such as where it is considered reasonably necessary in the interests of national security. There is a right of appeal against citizenship deprivation. Appeals take place at the First-tier Tribunal or (in national security/terrorism cases) the Special Immigration Appeals Commission, SIAC. In SIAC appeals, sensitive evidence may be withheld from the appellant and their lawyer, and a ‘special advocate’ appointed to represent their interests instead". The Supreme Court has given multiple judgments on how judges are required to handle appeals."
The first few paragraphs of your link are clear- ie that such Deprivation usually happens for national security reasons or in cases of fraud. Depriving someone of their British citizenship for the public good is generally used in the context of national security or counter-terrorism. The aim is to prevent a person who poses a threat to the United Kingdom from returning to the country, which they would otherwise have a right to do as a British citizen. There are also rare cases involving serious or organised criminals etc.
I stand by suggestion that investigation by police or security services would be required, covertly if there are national security concerns, to have evidence and ducks in a row for right to right to appeal, SIAC route if appropriate.