The term "a person subject to immigration control" is defined in Section 13(2) of the Asylum and Immigration Act 1996 as:
"a person who under the Immigration Act 1971 requires leave to enter or remain in the UK (whether or not such leave has been given)"
Generally speaking, this means anyone who requires a visa to enter or remain in the UK. It applies mainly to non EEA nationals but in Abdi & Ismail v. Barnet L.B.C.  EWCA Civ 383 the Court of Appeal held that EEA nationals who are not exercising a right to reside in the UK are subject to immigration control.
Section 7(1) of the Immigration Act 1988 provides that no leave to remain is required where a person has an enforceable right under EU law.
The position of European Economic Area (EEA) nationals is special. The Immigration Act 1971 does not apply to any person who has the right to reside in the UK either by virtue of Directive 2004/38/EC or the Immigration (European Economic Area) Regulations 2006 SI No. 1003. Therefore, an EEA national with a right to reside in the UK is not a person subject to immigration control.
Under the Immigration Act 1971, Section 2 and Section 3, and the Immigration Act 1988, everyone requires leave except:
(1) British citizens,
(2) certain Commonwealth citizens with the right to abode and
(3) EEA nationals exercising rights to reside.
(Also exempt are: diplomats, UK armed forces and forces visiting at the invitation of the UK government and crew of ships/aircraft due to depart within 7 days).
All other persons require leave and are therefore persons subject to immigration control.
An applicant who is subject to immigration control will only be eligible if he comes within one of the classes prescribed by regulation 5 of the Allocation of Housing and Homelessness (Eligibility) (England) Regulations 2006 SI No 1294.