United Kingdom statutes have never been officially codified; there is no United Kingdom counterpart to the United States Code. United Kingdom statutes are identified by the short title and the date of enactment.
Today, research on United Kingdom legislation is done online using the sources summarized here.
Legislation.gov.uk
This is the official website of UK legislation. It is administered by the National Archives. Legislation.gov.uk provides free access to Acts of the UK Parliament, Local Acts of the UK Parliament, and Measures of the General Synod of the Church of England. To use legislation.gov.uk, click on Browse Legislation, then click on UK Public General Acts.
Statutes are listed in reverse chronological order by year. Coverage from 1988 to the present is comprehensive. Coverage from 1801-1987 is not complete, but it is still quite good for more recent years. Legislation.gov.uk also has Acts of the Scottish Parliament and Acts of the Northern Ireland Assembly, as well as Measures of the National Assembly for Wales.
British and Irish Legal Information Institute (BAILII)
This free database includes legislation from the United Kingdom, Scotland, Northern Ireland and Wales. Legislation can be browsed alphabetically or chronologically for the UK, Ireland, Northern Ireland, Wales, and Scotland. To search for legislation in the database, use the Legislation Search form.
LexisNexis -- All United Kingdom Statutes & Legislation (LexisNexis subscription required)
Contains separate files for statutes and statutory instruments.
Westlaw -- United Kingdom Law in Force (Westlaw subscription required)
Contains separate files for statutes and statutory instruments.
Statutory instruments are roughly analogous to administrative regulations in the United States. Parliament may include in an act an enabling section, which grants to some other authority (usually a Minister of the Crown) power to make detailed rules and regulations on a principle laid down in general terms by the Act.
Statutory instruments are not codified. There is no equivalent of the Code of Federal Regulations in the United Kingdom. Statutory instruments are cited by short title and year of enactment, and are numbered sequentially during the year. An example is the Portability of Online Content Services Regulations 2018. This statutory instrument received the number 2018 No. 249.
Legislation.gov.uk
Legislation.gov.uk has a comprehensive collection of statutory instruments for the years 1987 to the present, and partial coverage for 1948-1986. There are also collections of statutory instruments for Scotland, Northern Ireland and Wales. This information is available on the UK Statutory Instruments page of Legislation.gov.uk.