That's a weird way to see history.

"the EU project"

You state this as though it is clear what this means. It was in fact Margaret Thatcher who insisted that the EEC implemented a common market. Your historical recividism concludes that the UK had nothing to do with this or resisted it.

The EUCHR was itself, in many ways, designed by the British. And yet you complain that a majority of politicians were and are not compatible with it?

The so-called commitment to the 4 freedoms is itself something of a reimagining of what the EU is. The free movement of services is only partially in effect, removing actual restrictions would require harmonising educational, professional and vocational education, licensing and regulation, amongst many other things. There is no "European Project" to achieve this.

One thing is certainly different about the UK vs several major European countries. There is no consensus in the UK that the "European Project" is essential to prevent devastating war on British soil. Many European countries rightly see the EU as the guarantee that they won't face another "European War" - at least not like those we saw in the 20th century. I don't think the UK shares the cultural pain, and the societal impetus to sustain the EU as the means to retaining this security. The UK never has needed mainland Europe in this regard, and was never really afraid to see the EU as primarily an economic alliance.