The official text of any treaty to which the UK is a signatory is published as a command paper. Command papers are a series of parliamentary papers and include other papers such as white papers as well. Command papers in the Bodleian Law Library are in the Parliamentary papers section on the ground floor and are arranged numerically and so you need to have the paper number.
Treaties are also included on the Foreign and Commonwealth Office UK Treaty Database and this is a very good place to start your search. This database has over 14,000 treaties available (10,000 bilateral agreements), from 1892-1996 you can access the full text of the treaty from this website. From 1997 onwards the treaties (as command papers) are available on a different service called Treaty Command Paper and EMs page. The UK treaty database has a search engine which allows you to search for the title of the treaty, treaty type, country or by date. There is guidance on how to search as well common acronyms and treaties that may be known as something else. After 1997 the treaties are listed either by date or alphabetically by subject but there is no search box. There is also a main list of treaties but these are on the more commonly asked themes such as Human Rights and Terrorism.
As the UK is a member of the UN, and is a signatory to the European Convention of Human Rights you may be able to get the text of treaties directly from these organisation. If you are having problems finding a treaty on the Foreign and Commonwealth Office databases it is worth going to the organisation that produced the treaty. See the list of links on the left hand side.