He is a confirmed Eurosceptic and cheerleader for Britain to exit the European Union. She is a Eurobuilder, a Swede who pushed for her nation to adopt the euro currency.

One has twice bid for national leadership, the other holds her cards in reserve. Both say they are staunchly for a global free trading environment.

Shortly after the June 23 referendum vote stunned the world by revealing a 52 to 48 per cent vote for Brexit, EU Trade Commissioner Cecilia Malmstrom made it clear that Europe was in no mood to forgive the recalcitrant for breaking away. It could not simply be business as usual.

"First you exit, and then you negotiate the terms of the relationship," she told the BBC, referring to post-Brexit trading arrangements.

That, countered Dr Liam Fox, the UK's Minister for International Trade, is "bizarre and stupid".

I had the privilege of interviewing both personalities separately over the fortnight past and asked Ms Malmstrom what she would have to say to Dr Fox if it was he, rather than I, talking to her. Her response was laced with more than a touch of European steel.

"Oh, I see him all the time but it would be the same as I have just told you," she said, eyes unblinking behind plastic frames at the end of a full day's meetings, which started soon after she stepped off the plane after the long flight from Brussels. "Mrs Theresa May has chosen to not be part of the single market or European customs union. That means a hard Brexit. Once it leaves, the UK will be a third country with whom we will have a totally independent FTA. But we will have to negotiate that."

At 48 and 55 years of age respectively, Ms Malmstrom and Dr Fox are of a European generation that was raised in the golden age of globalisation and liberalisation. Those ideologies are on the ropes now. The run-up to Brexit unleashed multiple emotions in Britain, and across the Channel, the continent is now feeling the tremors. Nationalism, fear of immigrants and other fissiparous pangs are tearing at the heart of the "ever closer together" European project.

Indeed, the UK vote probably had some influence on the US presidential election last November - Dr Fox denies this, seeing the Donald Trump victory as a revolt by middle America against the outsize influence of California and New York - and will reverberate in the Netherlands, France and Germany, key European states heading for their own national elections this year.

As I reminded Dr Fox, who looked uncomfortable when I mentioned it, not a single Asian economic power had wanted to see Britain exit the EU. Some, like Japan, explicitly warned against it. The ride ahead therefore promises to be a bumpy one, particularly for the leaver, evidenced in the sharp post-poll fall in the British pound. Indeed, some British politicians quickly resiled from their more outlandish claims after the referendum results were known. But what's done is done, and Europe and the wider world now have to pick up the pieces.

It is for this reason that Singapore played host to both Dr Fox and Ms Malmstrom, who has a doctorate in politics, in the space of a fortnight.

Both had good reason to be here. Few economies are as dependent on the outside world as Singapore, whose trade is about three times its gross domestic product. And while the island likes to say that its smallness compels it to accept the world as it finds it, Singapore has more than a little global influence. The EU would like to ensure that its attractiveness is not dimmed by losing the fifth biggest economy and the world's most global city, London. This week in Manila, she scored a small victory by initiating talks for an EU-Asean FTA.

For Britain, clinching a quick free trade agreement with Singapore soon after leaving the EU would be an immense feather in its cap, one to be waved around to show it can gain trade deals with non-EU powers, even if it is no longer part of the world's most successful regional integration project.

This is particularly so, since British outreach elsewhere hasn't been too successful. Last November, Prime Minister May flew to New Delhi, her first trip as national leader to a non-EU nation, to ask for a quick post-Brexit FTA. But the visit went poorly over immigration and student visa issues and she returned with little more than a cold stare from her counterpart Narendra Modi. Indeed, the EU-India FTA, a decade in the making, may progress faster once Britain exits the EU.

London may find more traction in Singapore, which tends to take a practical view of things. Hence, its urgency, even though it is leaving the EU, to see an EU-Singapore free trade agreement quickly in place. London thinks that it can dust off the EU document and get a similar one with Singapore.

"If the treaty has been ratified, we would want that to be the basis of a Singapore-UK FTA," Dr Fox told me, sitting in the drawing room of Eden Hall, the British High Commissioner's residence in Nassim Road. "If it hasn't been ratified, we will need a new FTA. We prefer that once a multilateral agreement is in place, we can make a transitional adoption where we treat all EU mentions (in the FTA document) as UK mentions. That would be a relatively simple thing to do because the body of negotiations will have been done."

Problem is, while negotiations on the FTA are concluded, the matter is stuck in the European court, which has to decide whether the deal can be ratified by just the European Parliament, or needs all 28 member states to agree. Indeed, burdensome bureaucratic and legal issues such as these are emblematic of the reasons why the British seek a future independent of the EU.

What happens to the UK? Will the parts that voted to stay in the EU wish to break away? I was in Edinburgh and St Andrews the week before the Brexit vote, and four out of five Scots I talked to were sure they were better off being in. Indeed, fear of losing access to the EU market was one reason why Scots voted to stay in the UK in a previous referendum. Now, fresh questions are rising in their minds.

Dr Fox, whose accent betrays his Scottish roots, says the current minority government in Scotland does not have the mandate to call for another referendum. Even if it were to come to another vote, he believes, Scots would still prefer to stay in the UK. Due to the collapse in oil prices, the Scottish economy would be even more vulnerable if it were to leave the UK. Besides, more goods from Scotland go into the UK than any other single market of the EU.

Scotland may be a small wrinkle when compared with what's looming for Europe. France, for instance, will hold presidential polls in April-May and far-right leader Marine Le Pen is making impressive strides in her bid for power.

Ms Malmstrom, who was partly educated at the Sorbonne and follows French politics closely, says it would be "very bad for France and Europe" if Ms Le Pen became president. "She stands for everything the EU does not stand for."

That said, France, as the founding light of the EU, may not be so eager to leave. "The Brits had a difficult relationship with EU since joining. They'd never wholeheartedly joined," she says. "There is discontent with EU in France as well, but it is of a different nature."

Dr Fox denies that politicians such as he have unleashed the darker instincts of their people. He pushed for Brexit, he says, because people who make the law must be accountable for people who live under it.

"Having our laws ultimately determined by European courts that are outside our control is unacceptable. The idea of people taking direct control is perfectly aligned to the times."

Europe would be foolish to attempt to punish Britain for its decision, he suggests, because it will impact the wider trading picture at a time when growth in global trade has stalled. Meanwhile, his own task is to return Britain to what's in its DNA - the outward-looking global trading nation it has always been.

Ms Malmstrom, meanwhile, is racing to stitch up free trade deals around the world. America's withdrawal from the Trans-Pacific Partnership Agreement has proved something of a boon in this regard, lending a new impetus to others in the TPP to seek alternative arrangements. A trade deal with Japan is almost through. An FTA with Vietnam should be tied down soon. Australia is further along the road, and so too are non-TPP members Indonesia and the Philippines.

It took some convincing by EU officials to convince the Swedish politician to stop in Singapore on her way to Manila. It was her first trip to the island and evidently one that both sides found useful.

It would not have surprised her to find that when it comes to pushing for globalisation, she was preaching to the converted. Perhaps that's why, in her meetings with Mr Tharman Shanmugaratnam, she found a lot of the conversation focusing on Sweden, as a well-informed Singapore Deputy Prime Minister pressed her on her country's domestic policy framework.

•Ravi Velloor's In Good Company alternates with Sumiko Tan's Lunch With Sumiko.