I think the EEC might be significantly smaller, for starters. It would keep a French-German axis (and the EEC name), rather than seek to be a "Union of Europe" as such - lacking Britain rather dents its ability to claim wider representative status. And if we're keeping a French-German axis, it is not impossible that German reunification never happens, because the sheer size of a united Germany would alter the balance of power within the smaller organisation.
I don't think Britain does much differently, apart from keeping closer economic links with the Commonwealth. It's one less thing for Margaret Thatcher to go crazy about.
The biggest butterflies are reserved for the likes of Australia and New Zealand. Both had the fun of losing a vital export destination overnight. If that never happens, you lessen the economic reform drive of the 1980s.
From browsing previous stuff, I think the Iberian countries (Spain and Portugal) would probably still join (especially Spain, who tried to join even under Franco in 1962!), as may Greece (if the junta falls like OTL).
I'm mixed over whether the ex-communist countries would want to join the EEC after the fall of communism in 1989...I think it depends on the country (ex. Baltics are more likely than say, Poland).
Along with UK, Ireland and Denmark joined as well OTL...I think from previous posts on this topic that Ireland won't join if UK don't, and Demark won't join at first (but may join later in the 80s because apparently West Germany would be their biggest trading partner by then).
I think the idea of a union was still present in the EEC...as another post said (paraphrasing) "The EEC was always meant to be a stepping stone to further integration. It was never a secret in mainland Europe. Only in the UK it was sold as just trade, and further integration as being just scary talk..."
I think German reunification still happens though...because the condition of East Germany was such that there was little chance of it continuing to survive...
Additionally, EFTA would still be around more, so that could serve as a bit of a rival to the EEC still...some of these ex-communist countries could join that instead...