The signatories of the Refugee Convention thought that some people didn’t deserve protection on account of having committed particularly heinous crimes. They therefore introduced “exclusion clauses”, found at Article 1F of the Convention. Accordingly,
The provisions of this Convention shall not apply to any person with respect to whom there are serious reasons for considering that:
(a) he has committed a crime against peace, a war crime, or a crime against humanity, as defined in the international instruments drawn up to make provision in respect of such crimes;
(b) he has committed a serious non-political crime outside the country of refuge prior to his admission to that country as a refugee;
(c) he has been guilty of acts contrary to the purposes and principles of the United Nations.
If you are looking for a detailed review of exclusion clauses 1F(a) and 1F(b), look no further than the case of KM (exclusion, Article 1F(a), Article 1F(b))  UKUT 125, The Upper Tribunal does an impressively deep dive into what constitutes a “crime against humanity” and “serious non-political crime”, and the tests used to assess when someone will fall under those exclusion clauses.
The conclusions in the case itself are quite fact-specific, but illustrate how difficult it is to be excluded from the Convention. This is for good reason: those excluded from the Convention lose the rights and benefits associated with refugee status.
The appellant, KM, had for several years worked in the Police d’Intervention Rapide (PIR) in Democratic Republic of Congo. While that organisation did commit crimes against humanity, the Upper Tribunal found that the Home Office was unable to show serious reasons for considering that KM had the requisite “individual criminal responsibility” to trigger the Article 1F(a) exclusion clause.
The tribunal found, however, that he had “knowingly aided and abetted in the torture of suspects” by arresting people during demonstrations and handing them over to the authorities. The tribunal found that KM would have known that such people could be tortured, and that this constituted a serious non-political crime for the purpose of Article 1F(b).
In practice, FM won’t be removed from the UK because it was accepted by all concerned that removing him would be a violation of his Article 3 rights under the European Convention on Human Rights (ECHR). The ECHR, unlike the Refugee Convention, does not contain exclusion clauses for non-derogable rights such as those protected by Article 3. In other words, if it is accepted that removing someone from the UK would violate their Article 3 rights, that person cannot be removed under any circumstances, no matter how arguably “undeserving” of protection they may be.