To an outsider, Britain means Brexit these days. Ever since the 2016 referendum, the country has been known for little else, as the twists and turns of a seismic shift in government policy have shaken both the internal arrangements and the external relations of the UK.

But a visit to these shores will illustrate two important counterpoints. Firstly, most people aren't living their lives in a state of constant engagement with the process of leaving the European Union (EU). Indeed, for many, it's a distraction from the day-to-day lives. The need to provide for their families, to have access to education, healthcare or welfare services, and the general desire to live their lives are much more present than the ins and outs of the withdrawal agreement, agreed this week.

In part that's because these other things are the basics of modern life, unavoidable and essential, whereas Brexit is seen as a matter of relatively abstract politics. In part, it's because the politicians seem to be making such a meal of it and seem so confused that there's probably no point in getting too interested: it's all a bit like hard work.

The second observation is that the British government still thinks it has to make sure that the rest of public policy continues to function and develop as in pre-Brexit times. And they'd be right: people don't stop getting ill, or needing education or infrastructure, just because of the end of UK membership of the EU. Life goes on.

You see echoes of this in government statements on tackling healthcare funding, or new initiatives on crime fighting or welfare payments. You also find it in British Prime Minister Theresa May's speeches and work: to read the 2017 general election manifesto of the Conservative Party was to witness something that looks a lot like politics-as-usual.

But this isn't a time for politics-as-usual. The reality of the situation is that May's government will be defined almost entirely by Brexit, rather than anything else it does (or doesn't) do.

The reason for this is simply that "Brexit" covers so much more than the narrow termination of being part of the EU. In leaving, the UK is discovering just how entangled and intertwined its political system and practices have become bound up with the Union's.

A key part of this is that it's a function of the length of membership: since 1973, not only has the remit of the EU grown massively, but the demands of modern economic and social practice have too – all states do a lot more than they used to.

As a result, there is no part of what the British state now goes that doesn't have to be reconsidered and reshaped by the removal of rules and regulations agreed within the European context. Ending membership means ending a series of practices and assumptions about how to do things.

That matters for a variety of reasons. It means that the entire work of government is colored strongly by the choices made on Brexit. If nothing else, there is an implication of changing financial and regulatory options that come with this, which will impact on even those bits of state activities that seem to be a long way away from the EU.

To take one big example, healthcare is not a well-developed EU competence, but we know already now that Brexit will have major implications for the NHS, from the likely drop in EU nationals working for it, to access to medicines, to changes in government funding because of the economic impact of leaving.

Besides, precisely because so much time and effort are being devoted to Brexit, there is relatively capacity to deal with anything else. Even major policy initiatives like the roll-out of Universal Credit, which has been very problematic, have been affected by this: much of the government's usual work is on a kind of standby mode, waiting for Westminster to find enough time to get back to the day job. Finally, the sheer scale of Brexit and its impacts requires there to be a national conversation about where this is all heading.

Much of the difficulty that the government has encountered stems from the lack of consensus about why the UK is leaving, how this fits into a bigger project for the country's future, both domestically and in the global system.

Maybe if May had had that debate with the country at the start of her premiership, then she might have been able to better contain and direct Brexit. Nevertheless, that didn't happen and so the UK is now bound to many more years of indecision and May is condemned to be the "Brexit PM", however this all turns out.