Here, I lay out, as I see them, the ten ideological groups of voters in Britain. I'd be interested in whether people agree with me, think I've missed one or think two or more ought to be merged. Not all of these groups are the same size; the Paternalist Right, the Traditionalist Left and The Centrists are probably the largest, with the Neo-liberals, Hard Left and Reactionaries probably the smallest.
The Hard Left
The Hard Left are socialist, reflexively opposed to overseas military action and theoretically in favour of internationalism but skeptical about the value of existing international institutions, including the EU. They are social progressives; comfortable with the increasingly multicultural nature of Britain and the increased visibility and status of LGBT people. They are, however, not hardcore social liberals, being in favor of government intervention to protect the rights of animals, promote environmentalism, support minorities and improve public health, even if this entails a degree of interference with individual freedoms.
During the New Labour years, some parts of the Hard Left abandoned Labour, transferring support to the Greens or one of the churning mass of similarly named socialist parties on the left of British politics. They seem to have returned to the fold now that one of their own leads the Labour party. Jeremy Corbyn and his close allies are of this tribe.
The Liberal Left
The Liberal Left are social democrats, skeptical of overseas military action and probably the most ardent champions of internationalism, being very much in support of remaining in the EU. They are socially progressive and liberal, in favor of government intervention to protect minorities, but also wary about the degree to which this might impede upon freedom of speech and expression. They tend to be extremely concerned about the government accruing powers that prevent oversight or silence critics.
The Liberal Left has always been divided between Labour and the Lib Dems. Blair's tenure as leader of the Labour party caused a flow out of Labour and towards the Lib Dems and Greens while the Coalition caused a catastrophic flow away from the Lib Dems and towards the Greens and Labour. Inside Labour, the Liberal Left represents the "soft" portion of Jeremy Corbyn's support. Caroline Lucas is on the left side of this tribe, while Charles Kennedy was on the right side of it.
The Traditionalist Left
The Traditionalist Left are social democrats and skeptical of both overseas military action and internationalism, generally favoring leaving the EU. They are socially conservative and are concerned and sometimes angry about the rate of immigration and ambivalent about the increased visibility and status of LGBT people (often manifesting as acceptance of gay people, but skepticism about bisexuals and trans people). They support government intervention to preserve or restore the nature of Britain, but not to change it. They are ambivalent about welfare, feeling that too much is given to the "undeserving", but wanting more help available to the "deserving".
The Traditionalist Left were, for a long time, taken for granted by Labour. Many of them stopped voting Labour during Blair's leadership without necessarily transferring their support elsewhere. More recently, many of them have begun voting UKIP. Nevertheless, they continue to make up a large slice of Labour's vote. They are not well-represented in terms of MPs or front-benchers, despite being a significantly sized group of voters.
The Paternalist Left
The Paternalist Left are social democrats, tend to judge cases of overseas military action individually and favor internationalism and the EU. They, like the Hard Left, are socially progressive but not unreservedly socially liberal. They are happy for the government to intervene to protect public health and promote environmentalism, but less inclined than the Hard Left to want the government to intervene in an attempt to create social change. They are also more security-minded than the Hard Left or Liberal Left and are willing to see some degree of individual liberty curtailed in order to uphold collective security.
The Paternalist Left are solidly aligned with Labour. Alan Johnson and Hillary Benn are probably the most high-profile figures associated with this tribe. Tony Blair straddled the divide between the Paternalist Left and the Neo-Liberals.
The Centrists are, as their name implies, centrist with regard to economic policy. They tend to favour overseas military action at the onset and regret it later. They are undecided about internationalism and the EU. They are mildly socially progressive, more so with regard to LGBT people than with regard to ethnic minorities (especially South Asians/Muslims). They are concerned, rather than angry, about immigration and think it should be reduced. They are mildly socially liberal, more in favor of government intervention to uphold public security than to protect public health.
The Centrists are, as you would imagine, swing voters. They mostly voted Labour in 1997 and 2001, mostly voted Tory in 2010 and 2015.
The Neo-liberals are slightly to right of centre on economics, tend to favour overseas military action, internationalism and the EU. They are socially progressive and liberal and are relaxed about high immigration. This tribe seems to have the force of international consensus behind it; international treaties are often of a strongly neo-liberal bent.
Nick Clegg and George Osborne are Neo-liberals, while David Cameron straddles this tribe and the Paternalist Right. Neo-liberal voters tend to split evenly between the Conservatives and the Lib Dems currently, though many voted Labour in 1997 and 2001. Tony Blair straddled the divide between the Paternalist Left and the Neo-Liberals.
The Classical Liberals
The Classical Liberals are right-wing economically, tend to judge overseas military action on its merits and are opposed to internationalism and the EU. They are socially liberal but ambivalent about progressivism; generally being in favor of equal treatment under the law, but against government trying to regulate social attitudes. Their intellectual tradition pushes them towards a relaxed attitude to immigration, but the realities of choosing political bed-fellows pushes them towards an anti-immigration attitude. Often advocacy for more non-EU immigration and less EU immigration is used to square this circle.
Classical Liberals divide between the Conservatives and UKIP, with a tiny Euroskeptic movement within the Liberal Democrats. Douglas Carswell and David Davis are Classical Liberals.
The Paternalist Right
The Paternalist Right are moderately right-wing economically, tend to support overseas military action and are ambivalent about internationalism, but are broadly in favour of the EU. They are moderate social conservatives, favoring a strong, protective state that prioritizes keeping its citizens safe. They are lukewarm about the interests of sexual and ethnic minorities. They support reducing immigration.
The Paternalist Right is solidly aligned with the Conservative party. Ken Clarke is of the Paternalist Right and David Cameron straddles the Paternalist Right/Neo-liberal divide. Also called One Nation Tories or "wets"
The Free Market Authoritarians
The Free Market Authoritarians are hard-right economically, support military action overseas and oppose internationalism and the EU. They are full-throated social conservatives and oppose social progressivism. They support empowering the state as much as is necessary to ensure national security. They support reducing immigration.
The Free Market Authoritarians, previously having been stalwart supporters of the Conservative party, have begun being poached by UKIP. Jacob-Rees Mogg and Michael Howard are Free Market Authoritarians, as was Margaret Thatcher. Generally known as Thatcherites or "dries".
The Reactionaries are economically protectionist, oppose military action overseas and are implacably and furiously opposed to internationalism and the EU. They are socially conservative and view social progressivism as a moral evil. They are in favor of using the power of the state to substantially revert the last 60 years or so of changes to British society. They want a complete halt on immigration and, in many cases, a program of repatriation. They are, to be candid, racist and in most cases also sexist and homophobic.
The Reactionaries previously voted for a variety of hard right and fascist parties, if they voted at all. Most of them now vote for UKIP (although they do not make up a majority of UKIP voters). Nick Griffin, Katie Hopkins and Paul Nuttal are Reactionaries.