Stateless Person is defined under part 14 of the Immigration Rules.

Paragraph 401 of the Immigration Rules describe stateless person as follows

For the purposes of this Part a stateless person is a person who:

1. (a) satisfies the requirements of Article 1(1) of the 1954 United Nations Convention relating to the Status of Stateless Persons, as a person who is not considered as a national by any State under the operation of its law;

2. (b) is in the United Kingdom; and

3. (c) is not excluded from recognition as a Stateless person under paragraph 402

Who is Excluded from Recognition as a Stateless Person? 
Paragraph 402 of the Immigration Rules states a person is excluded from recognition as a stateless person if there are serious reasons for considering that they:

1. (a) Are at present receiving from organs or agencies of the United Nations, other than the United Nations High Commissioner for Refugees, protection or assistance, so long as they are receiving such protection or assistance;

2. (b) Are recognised by the competent authorities of the country of their former habitual residence as having the rights and obligations which are attached to the possession of the nationality of that country;

3. (c) Have committed a crime against peace, a war crime, or a crime against humanity, as defined in the international instruments drawn up to make provisions in respect of such crimes;

4. (d) Have committed a serious non-political crime outside the UK prior to their arrival in the UK;

5. (e) Have been guilty of acts contrary to the purposes and principles of the United Nations

Stateless Person to ILR (Indefinite Leave to Remain):
Paragraph 403 of the Immigration Rules. The requirements for leave to remain in the United Kingdom as a stateless person are that the applicant: