You would need to prevent euroscepticism from surfacing in the major parties on a larger scale than other EU member states. One possibility would be for Britain to lose the Falklands War. Not only that would deal a blow to Britain's view of itself as a major power, thereby increasing a willingness to see Europe as the future, but it would also turn the wind in favour of centrists, who tended to be much more pro europe. Thatcher would go, and may well be replaced with a One Nation Tory like Heseltine. It would also make the Tories even more unpopular, leading to a boost for the SDP-Liberal Alliance, who were unequivocally pro Europe.
They could defeat Labour, and possibly even the Tories, in the popular vote at the next election, and set themselves on the path to becoming one of the main two parties. Within a few decades, you could see a Tory party that remains firmly one nation having had a disastrous experiment with Thatcherism, along with the Europhile Alliance parties, and a Labour Party which is firmly on the left but reduced to third party status, taking a 'remain and reform' approach to it.
Of course, if your going to have a PoD after 1900, Britain (or at least England) is always likely to be at least a bit more eurosceptic than the rest of the continent, but if you limit the appetite for a referendum within the main parties, then it becomes a lot less likely any major steps toward leaving would be made.
Maybe whatever it is that causes Scotland and Ireland to be pro Eu, could happen to England?
As has been identified already that is most likely down to a view of the world that is more anti imperialist than an island mentality that England has. They are more willing to see themselves as small nations who might need to work with other countries to get by rather than as a major player on the world stage. To change those things would probably require a PoD going back way before 1900.