What policy divisions are there within the Conservatives?

Marriage (Same Sex Couples) Act 2013 – 118 Conservative MPs in favour, 129 against (Free vote) This free vote on same-sex marriage highlights the divisions that exist between the Conservative Party’s more religious, traditionally conservative, members, and its more socially liberal members.
Former Prime Minister David Cameron often described himself as a ‘liberal conservative’, who supports not only the economic liberalism of Thatcher, but also a more liberal attitude to social issues as well, such as same-sex marriage.
However, many religious social conservatives opposed this change to the traditional definition of marriage.

EU Referendum Debate (October 2015) – 81 Conservative MPs support a motion in support of a referendum Although David Cameron insisted that his party had to stop “banging on about Europe”, this large rebellion helped lead to his 2013 Bloomberg speech, in which he finally promised an EU referendum after the 2015 General Election. For some Conservatives, like Cameron, the EU “matters for British jobs and British security”. However, more traditional Conservatives objected to the EU’s impact on Parliamentary sovereignty and immigration levels.
They argued that when Edward Heath’s Conservative Government joined the EEC in 1973, the party was supporting free trade, not political union.
For the 2016 EU referendum, David Cameron suspended collective responsibility. As the 2016 EU referendum has settled the question of whether or not the UK should withdraw from the EU, the party has since become much more unified.

House of Lords Reform Bill 2012 – 91 Conservative MPs rebel, helping to defeat the Coalition’s reforms While more liberal, modernising Conservatives found it easier to work with the Liberal Democrats, and were more supportive of constitutional reform, other more traditional Conservatives are strongly opposed to sweeping reforms to traditional institutions, and were unwilling to support the Coalition’s plans for a newly elected House of Lords.
This rebellion was the largest rebellion by Government MPs on the second reading of any bill since 1945 and led to a considerable increase in tensions between the two Coalition parties.