Britain's entry into the EU had been blocked by opposition from French President Charles de Gaulle. Once de Gaulle resigned in 1969, however, the ball really began rolling on accession.
The Tories, who were led at the time by Ted Heath (a moderate on socioeconomics compared to "new right" types like Maggot Thatcher), were mostly in favor of accession thanks in part to heavy corporate lobbying. Labour, on the other hand, was split because many feared that increased competition from more industrialized countries such as France, Germany, Sweden, and to some degree Italy, would cost British jobs. There were also concerns over loss of sovereignty, which appealed to nationalists on both sides.
One particularly nationalist (some would say racist) Tory MP, Enoch Powell, even endorsed Labour in the 1974 elections out of his belief that a Harold Wilson government would lead Britain out of the EU. This, of course, never happened - in large part because when the oil shock plunged Britain into a deep recession (the pre-North Sea oil UK was hit harder than most developed countries), exports to the more bouyant continental market became crucial to mitigating the impact of recession (which they did).
Today, however, Britain keeps large and growing trade deficits with the rest of the EU - £24 billion ($35 billion) in the first quarter of 2016 alone - and that has certainly exacerbated euroscepticism in the UK.
It's a lot more complicated than just that, of course, and I'm sure some of our resident British contributors could elaborate further.
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