Some of them are obsolete or not used very often. I think the relevant ones nowadays are as follows:
BC- British citizen. (UKC may also be used - UK Citizen)
BRP - Biometric Residence Permit. A credit card sized plastic document that serves as one's visa.
CIO - Chief Immigration Officer. A senior immigration officer (see IO, below) based at UK ports.
CP- Civil partnership.
CTA - Common Travel Area. The geographic area including the United Kingdom, the Republic of Ireland, the Isle of Man, and the Channel Islands (Jersey and Guernsey.) In most cases, there are no immigration checks when traveling wholly within the CTA. UK nationals are able to freely travel thoughout the CTA, but those of other nationalities (including holders of UK visas) may have to obtain visas to enter/reside in other parts of the CTA.
EC - Entry clearance. Provides permission to travel to the UK for a specific purpose (ie marriage, visit, study, work, etc.).
ECO - Entry Clearance Officer. Approves/rejects UK visa applications.
EEA - European Economic Area. Includes all of the member states of the
European Union (EU), along with Norway, Liechtenstein, and Iceland. Citizens of these countries do not need visas to live and work in the UK (although they may need work authorization if they are a citizen of one of the newer EU member states.) Switzerland is not part of the EEA, but its citizens have the same right to live/work freely in the UK as EEA nationals. The UK immigration forms applicable to EEA & Swiss citizens and their families are numbered EEA1-4.
FLR - Further Leave to Remain. Time-limited permission to remain in the UK for any number of reasons, granted to someone who is already residing in the UK on another visa. FLR can be granted for a number of categories (with restrictions), including studies, work, marriage, or as a dependent of another UK visa holder. FLR normally comes with a blanket prohibition on accessing Public Funds, or "benefits."
FLR(M)- the name of the form used to apply for Further Leave to Remain on the basis of marriage/partnership to a permanent resident of the UK or a British citizen. Can be used by spouses, civil partners and unmarried partners, depending on the circumstances.
HO - Home Office, a large part of the UK government responsible for several functions including immigration.
ICT - Intra-Company Transfer (part of the Tier 2 category). When a company wishes to sponsor an employee to move to the UK working within the same company. This type of visa does NOT lead to permanent residence.
IHS - Immigration Health Surcharge. An extra fee required for certain visa applications that allows the visa-holder to access the NHS in the UK.
ILPA - Immigration Law Practicioners' Association. A professional association of immigration lawyers, advisers and other practicioners who work within the field of UK immigration law.
ILR - Indefinite Leave to Remain. Permission to remain in the UK indefinitely, with no time limit attached ("permanent residence.") Allows full access to public funds. Can be lost if the holder resides outside the UK for more than 2 years.
IO - Immigration Officer. Inspects passports, conducts entry interviews, and controls access into the UK at all UK ports. In the case of non-visa national visitors, issues visit visas at the port through a six-month passport stamp.
KOL - Knowledge of Life/Language. Refers to the requirement to demonstrate knowledge of the English language and knowledge of life in the UK for ILR applicants (introduced April 2007) and applicants for citizenship who received ILR before April 2007. These requirements can be fulfilled by passing the Life in the UK Test. May also be referred to as LIUK (Life in the UK) test.
LLR - Limited Leave to Remain. Permission to remain in the UK for a limited time period. Usually used interchangably with Further Leave to Remain (FLR).
LTR - general shorthand for Leave to Remain.
OISC - Office of the Immigration Services Commissioner. Regulates UK immigration advisers who are not regulated by another professional body (eg the Law Society.)
SET(M) - The form used to apply for Indefinite Leave to Remain (ILR) on the basis of marriage/partnership to a UK permanent resident or British citizen. SET denotes settlement. Variations could include SET(LR) - applying for settlement on the basis of long residence (LR) or SET(DV) - applying for settlement on the basis of domestic violence (DV).
UKM - the application form used to claim British nationality through a British mother- applies to those born between 7 February 1961 and 1 January 1983.
UKVI - UK Visas and Immigration. The department of the Home Office responsible for visas. Was previously known as the UKBA (UK Border Agency).
UP - Unmarried Partner. For immigration purposes, a partner of a UK permanent resident, British citizen, EEA citizen or work permit/HSMP holder who can prove two years of cohabitation in order to obtain a UK unmarried partner visa, EEA residence card, or dependent visa.
VAF - Visa Application Form.
WP - Work Permit. An immigration document (applied for by the sponsoring company) that allows the holder to come to the UK to work in a specific job at a specific employer for a limited time period (up to 5 years.) If a WP holder wishes to change jobs, a new work permit must be applied for by the new employer. Work permits are divided into multiple categories (e.g. Tier 1 Investor, Tier 1 Entrepreneur, Tier 2 ICT, Tier 2).
If there are ones you've seen not on the list, feel free to post them here and hopefully we'll be able to help out.
ETA: Added the IHS acronym, as I realized later it had been completely omitted.
