Prior to the 1979 Election (Which brought in the 'Thatcherite' Conservative party under Margaret Thatcher herself), the British political establishment was essentially two sides of the same coin: The post-war consensus of Keynesian economics (nationalisations), full employment, nuclear deterrence, a special relationship with the US, and a maintenance of the British welfare state setup by Attlee's 1945-51 Labour government (The NHS being the shining symbol of this) were adopted by both the Tories and Labour - The Conservatives won three elections in the 1950s - 1951, 1955, and 1959, each time increasing their majority - But they only ever denationalised iron and steel (in 1951). The reason for the creation of this consensus was manifold - The Tories feared being known as the 'party of unemployment' - They were the party primarily in power during the Great Depression, and the new welfare policies (Social housing, the NHS, the new education system (The Beveridge Report was the document that primarily inspired the British welfare system)) were incredibly popular with the electorate.

Britain didn't join the EU (I'll refer to it as the EU throughout, although the time you're referring to it goes through multiple names) when invited in 1955 to sign the Treaty of Rome, over fears that it would impact food import costs from the Commonwealth and a feeling that we didn't need European goods - There was a post-war boom as British industry filled the world's shops.

The irony of this was of course that the losing nations - Germany, Japan, and even Italy to an extent, soon began to rebuild their industry - With newer, modern manufacturing methods - And the nationalised industries of the UK, with no fear of losing jobs or competition internally, began to lag behind in efficiency.

Britain applied twice in the 1960s to join the EU (In 1963 under the Tories, and in 1967 under Labour), and both times it was vetoed by Charles de Gaulle, who feared that Britain would assert itself in continental affairs, and, due to the Special Relationship, bring undue American influence, when France could become the leading nation within Europe.

Joining the EU was seen as a way of mitigating the decline of the British economy, by joining a trading bloc, and in the 1973 under Edward Heath (Conservative), the UK did join the bloc. However, the left-wing of the Labour party (Tony Benn for example) believed that cheap European goods would undermine British industry and hurt British workers, and so opposed Britain being in the EU.

In 1975 the Wilson government held a referendum on British membership of the EU, with 67% voting to remain in Europe.

Enter Margaret Thatcher. Thatcher's economic positions lead to her signing the Single European Act in 1986, creating the free trade area known today as the 'Common Market'. However, she was always standoffish with European leaders themselves - Sceptical of the Delors report (the infamous Sun headline 'Up yours Delors') which recommended moving towards a single currency. By the timed she was ousted from office in 1990, Thatcher's opinion on Europe had soured, and the members of her cabinet who most virulently opposed her were generally the most Europhilic - Ken Clarke and Geoffrey Howe.

Meanwhile, after the 1979 defeat of Labour at the polls, after the disastrous 'winter of discontent' (The largest strike by British trade unions since the 1926 General Strike) the Labour party, under Michael Foot, was influenced by Tony Benn and the growing 'Militant Tendency' (A socialist movement) to swing even further left - Gerald Kaufman, a Labour MP, termed the Labour 1983 manifesto the 'Longest suicide note in history' - Unilateral nuclear disarmament, re-nationalisation of privatised industries, abolition of the Lords and leaving the EU.

In reaction to their stunning defeat (Their vote was split between Labour and the new Social Democratic Party, or SDP - Former Labour MPs who disliked the leftwards swing) in 1983, the Labour party elected leader Neil Kinnock.

Kinnock, over the course of the 1980s and what is termed Labour's 'wilderness years', dragged the party back to the centre-ground - And as part of this, adopted a Europhile stance.

In 1992, Britain joined the Maastricht Treaty, which called for closer European integration - Tory rebels tried to block Britain joining, as there were fears over the influence of Brussels in the UK, stoked by former Prime Minister, and now Lady, Thatcher herself.

By 1997, the election of Tony Blair, the Conservative party was split between a strong Eurosceptic and strong Europhilic wing, mostly along the lines of hardliners and moderates respectively - The Tory PM John Major resigned in 1995 and called a leadership challenge against himself which was answered by Eurosceptic John Redwood. Redwood lost, only securing 89 votes to Major's 216. Labour meanwhile had moved much closer to the Conservative position, with Blair being highly Europhilic.

To summarise: In the 1970s Labour feared that it would harm British jobs, while the Tories thought it would boost the British economy. By the 1990s The Tories right-wing then believed it was beginning to infringe on British sovereignty, while Labour believed it was part of being a more centrist, consensual position politically.

Sources:

A-Level 'Britain 1951-2007'

Andrew Marr's 'A History of Modern Britain'

u/theGentlemanlyMan alluded to it briefly, but many writers have suggested that Jacques Delors single-handedly created modern British political attitudes to Europe.

So, in September 1988 Jacques Delors gave a speech at the annual British trade union congress. Delors, was known as hard working, Catholic, and fairly right-wing when it came to monetary policies. He was also former chairman of Evian European Council which was set up to discuss European monetary union, and was an enemy of the French Communist Party. In his speech he challenged Margaret Thatcher to aid Europe in creating a union that preserved workers rights, ensured collective bargaining agreements, and extended the luxury of lifelong education to everyone. The British trade union members and assembled guests responded favorably to this description of a future social democratic European Union, and spontaneously burst into Frere Jacques and traditional miners songs.

Margaret Thatcher was not impressed, and shortly thereafter responded with her now infamous Bruges Speech, where she famously stated that the frontiers of the state has not been rolled back in Britain only to be re-imposed by Brussels. The formerly pro-European and pro-business Conservative party became incensed at Delors’ exhortation for stronger trade unions, and seized upon an off-the-cuff remark he had made earlier that year about 80% of European laws being decided in Brussels by 1998, a remark which was not sanctioned by any other European bureaucrat, official, or politicians, and which Delors is said to have immediately regretted.

The Tories and Thatcherism were formerly pro-Eu and pro-business, but these speeches and phrases from Delors implied that the EU was set on instituting policies that were firmly against Thatcherism. To be fair, Thatcher, Major, and the leading Euro-sceptics of the day were never against the Eu, or British membership, they were against a social democratic form of Europe that removed laws from Britain and gave an increased focus on social rights at the expense of taxpayers. Thatcher even said:

Let me be quite clear: Britain does not dream of some cosy, isolated existence on the fringes of the European Community. Our destiny is in Europe, as part of the Community.

But they had not been working to "roll back the state" only to have that state reimposed by legislation from Europe.

The Labour movement also changed they attitude to Europe because of this speech. Between 1950 and 1975, the TUC had favoured negotiation on terms of membership, or even outright withdrawal from Europe. The 1980 Annual Congress Report was mixed, but still recommended withdrawing. However, from 1988 the Annual Congress Reports have all favoured conditional, or total support for membership. This is attributed to the "social dimension" that Delors alluded to, and which Thatcher hated. It's a similar trend with the Labout Party. Their traditional opposition to Europe was because it was seen as an anti-union, anti-workers rights free market, but Delors convinced the party that there was a concerted push for workers rights and freedom.

It is said that “(if) Delors had thought more carefully about the impact of his speeches in the summer of 1988 and if Thatcher had patronized Delors giving moderate and useful advice to British trade union, perhaps history would have been different[1].”

European and British culture have always been at odds with each other, but never more so than following Delors’ speech. The Conservative Party’s opposition has only increased since, and they have gone from being the Party of Business and Europe to frantically trying to claw voters and MP’s back from UKIP. The change to Labour and the wider Trade Union movement has been equally severe; from attacking Europe for being run by and for bankers and corporations, to the full support offered from Tony Blair and Gordon Brown.

[1] MacShane, (2016) Brexit: How Britain Left Europe p.69

Philip B. Whyman (2008) British trade unions, the 1975 European Referendum and its legacy, Labor History, 49:1, 23-45