The relationship between the EU and the UK has been rocky from the get go.
Prior to joining, the UK had initially passed on joining the EEC in 1957. It reconsidered shortly after but de Gaulle, anticipating a mismatch, vetoed their joining twice; his departure cleared the way to the UK finally joining in 1973.
De Gaulle had good foresight: the UK negotiated a permanent rebate to its budget contribution in short order, opted out of the Schengen zone, opted out from the Euro, and has had a long tradition of resisting anything that resembled deeper integration within a European Superstate or expanding consumer protection or social welfare. In the UK mindset the EU has always been about a common market and that only.
In terms of practical changes, entering the EU meant accepting past agreements, the existing (and future) body of European law, European institutions including the EC and the ECJ, and financial contributions. It also meant some loss of sovereignty.
The loss of sovereignty was most visible in the sense that European national parliaments spend quite a bit of time transcribing Directives passed in Brussels (and Strasbourg) into local law. An (in my opinion) unfortunate side effect of this reality is European governments periodically haggling with each other at the EU level in order to push desirable reforms forward, having Brussels write and pass Directives to their effect, and then claiming at home that it's all Brussel's fault as they dutifully transcribe them into local law without taking too much heat. Leaving aside that this makes the EC a very convenient scapegoat, it feeds into the notion that the EU is undemocratic, when in reality the member States do have have - if only informal - influence on what's going on in the EC, and the EP can and does rebuke EU laws it doesn't like. Lobbying and lack of EU news coverage further exacerbate the sentiments of lack of scrutiny and loss of control.
The other visible aspect of the loss of sovereignty revolved around foreign policy. Since the treaty of Rome (a few years earlier, in fact), European member states have had representatives in charge of doing some common diplomatic missions on their behalf - chiefly to negotiate their commercial interests as a single block. The exact nature of the Union's diplomacy boss changed over time. To the UK this has been a distasteful loss of control from the get go.
With respect to foreign policy, the EU also has traditionally striven to speak as a single voice on the international scene, and the UK hasn't always played along. In the UK's defense, it's not alone in doing so. France in particular also mourns its past grandeur and likes playing Great Power too. But their coping mechanisms differ. In some sense, France pumps its chest on the international scene, fantasizing as it may that its own views and interests are in fact those of Europe at large. They get a vitriolic rebuttal from time to time. And to the extent that they coordinate with Berlin one could also suggest that they're inter-mediating Germany's diplomacy to some degree. The UK, by contrast, has traditionally been somewhat more confrontational and aligned with US interests. The contrast between the two attitudes was painfully visible during the run up to the second Iraq War. The UK aligned with the US in a heart beat. France led the EU's old guard at the side of Germany and denounced US warmongering at the UN. And EU's newer members ended up supporting the US provided it got UN approval. Illustrating France's tendency to conflate its own diplomacy with that of Europe, Jacques Chirac let go of a scathing: "It is not well brought up behavior. They missed a good opportunity to keep quiet."