It is hard to discuss the result of the UK's referendum on its EU membership without, in the first sentence, using the word "uncertainty": there are so many questions to which no-one knows the answer, and many plausible scenarios that could play out in the coming years. That uncertainty will, undoubtedly, be damaging for many businesses, and for the European economy – but, although the negotiations over the terms of the UK's withdrawal and its future relationship with the rest of the EU will take years, there are some issues which could be resolved more quickly. It would be in the interests of all EU citizens and businesses to prioritise those.

One such issue concerns the rights of non-UK EU citizens who are currently living and working in Britain and, conversely, the rights of Brits who have settled elsewhere in the EU. The current uncertainty extends beyond just whether a person will be entitled to remain in the country in which they currently reside, but also whether they will continue to enjoy equal access to healthcare and other services, and to non-discriminatory treatment more generally. These are vital questions for many businesses, including, of course, private equity and venture capital fund managers and their portfolio companies right across Europe.

Among UK politicians – indeed, even among the two remaining contenders to be Britain's next prime minister – there are two schools of thought: one, that the right of EU citizens to remain in the UK indefinitely, if they are already here, should be guaranteed now, unilaterally; others take the view that their status (including their other entitlements) is an issue which forms part of the overall negotiation, and should not be conceded without reciprocal rights being granted to UK expats living in the EU. The former position was taken by the House of Commons this week, in a non-binding motion backed by 245 MPs, while the latter position has been endorsed by the present government, whose Foreign Secretary asserted that it would be "absurd" to give any guarantees without getting a reciprocal promise. The government has, however, made very reassuring noises about its intentions, and re-stated that those who have already been in the UK legally for five years will, as now, have a right to remain.

It seems inconceivable that EU nationals who are currently living and working in any EU country will be sent home after the UK leaves, although it is hard – when so many unlikely scenarios suddenly seem plausible – to rule anything out. But the economic costs and practical difficulties of removing people would be enormous, and could even be ruled illegal under domestic or international law (although the legal arguments are far from clear, and could vary depending upon individual circumstances – compounding the practical issues that would need to be resolved). It is not therefore a very convincing "bargaining chip" for either side in the negotiations while, on the other hand, there is much to gain from clarity. Some baseline assurances would be welcome, even if they left some questions open.

Moreover, the context for the coming negotiations is vital, and thinking about them as "divorce" proceedings (amicable or otherwise) is unhelpful. The UK and the EU – and, vitally, their respective businesses and citizens – will need to work in partnership in the coming years, whatever the precise terms of the trade deal that is reached. Inevitably, protecting national interests will be critical, but negotiators on both sides should take an enlightened view of those interests, and unilateral "concessions" might actually help in the longer term.

It is for the politicians across Europe to decide the best way to resolve this issue, but there is much to recommend its early resolution – and delay will not serve the continent of Europe well. Fortunately, to most people, the principle that should determine the outcome will seem pretty clear, even if there are some points of detail to hammer out (including which date to choose as the cut-off). In the meantime, employers need to be careful not to discriminate against other EU nationals, which remains illegal, but can surely be confident that legal migrants will not one day be deported.