The British Antarctic Territory (BAT) is the largest British Overseas Territory by area, but has no indigenous population. This, the BAT page of the GOV.UK site, provides information on the administration of the Territory and on the Antarctic Treaty, with link to the full text.
The Falkland Islands Government site contains the new Constitution (in operation from 1 January 2009) accompanied by an account of the differences between it and the former constitution of 1985. The Legislative Assembly section provides verbatim reports of Assembly sittings, 2007 onwards: these are within the subsection “Public Papers”. For legislation, see the separate Falkland Islands Statute Law Database.
The Statute Law Database is maintained by the Statute Law Commissioner and describes itself as “an authoritative statement of the legislation applying to or in relation to the Falkland Islands by Ordinance”. It contains Ordinances, secondary legislation, United Kingdom laws and European Union laws as in force in the Falkland Islands. Legislation made after 31 July 2017 is also included in the form in which it was made.
South Georgia & the South Sandwich Islands (SGSSI) have been a self-governing Overseas Territory of the United Kingdom since 1985. From 1908 to 1985 they were dependencies of the Falkland Islands. The SGSSI Government web site contains legislation (Ordinances and SROs) from 1908 onwards, those of the period 1908 to 1950 being in the form of scans (PDF) taken from Laws of the Colony of the Falkland Islands and its Dependencies (revised edition, 1951). There are also links to the Falkland Islands Statute Law Database and the UK’s legislation web site.
St Helena, Ascension and Tristan da Cunha are internally self-governing Overseas Territories of the United Kingdom. This Legislation section of the St Helena Government website contains the latest edition of the Revised Laws for each of the three territories, all dated 2017. Individual laws are available in PDF.