There is no definitive list of "mainstream" denominations in the UK - indeed the term is largely subjective - but there are a number of official and semi-official ways in which denominations are recognised.
The NHS Data Dictionary, based on the international Systematized Nomenclature of Medicine Clinical Terms (SNOMED CT), lists some 80 possible values for Christian religious affiliation - but since this is an international list it is not specific to Britain.
Some denominations self-identify as being mainstream; the URC website says:
Although one of the smaller mainstream denominations, the United
Reformed Church plays a dynamic and challenging part in the British
Wikipedia provides a comprehensive list of denominations in the UK, categorised into 12 groups (including "interchurch" - ie pan-denominational groups, and Catholicism) but does not indicate which are "mainstream". The twelve groups are:
Holiness & Pietist
Methodist & Wesleyan
New Church Movement
Presbyterian & Reformed
The Methodist Church website contains a basic introduction to Christian denominations which contains some links to some other useful resources. The World Council of Churches lists 11 member churches that are based in the UK while Churches Together in Britain and Ireland lists several more member churches. Since none of these lists are an exact match for one another it is fairly clear that no definitive list exists, but that lots of denominations are "recognised" by some larger organisations.
What constitutes "official" could also be somewhat subjective. It is well known that the Church of England is the officially established church in England. The Church of Scotland, Church in Wales and Church of Ireland are not, however, officially established. (The Church of Scotland is an unusual case where some official documentation implies the church is officially established, but the church themselves disclaim this.) (Source: good old Wikipedia)
Nevertheless there have been a number of Acts of Parliament relating to individual denominations; this does not of course make them official state churches, but does at least show that they are recognised by the state. Examples include:
- Protestant Religion and Presbyterian Church Act 1707
- Methodist Church Union Act 1929 / Methodist Church Act 1939 / Methodist Church Funds Act 1960 / Methodist Church Act 1976
- Salvation Army Act 1931 / Salvation Army Property Trust Act 1934