Two weeks ago the Home Office told the Sunday papers that the new “points-based system” for immigration after Brexit would cut unskilled immigration from the EU by 90,000 “overnight”. And today the government has published more detail about its proposals, generating headlines such as “Immigration revolution” and “UK closes border to unskilled workers”.

In fact, there’s less here than meets the eye. Free movement will indeed end when the Brexit transition expires next January – but that’s been government policy for more than three years. For the vast majority of new migrants, despite the branding, this isn’t really a “points-based system” in any meaningful sense, still less an “Australian-style one”. Broadly, the government has accepted the recommendations of the independent migration advisory committee for the new system. There will be a salary threshold for migrants coming here to work – whether from inside or outside the EU – of £25,600 (more for those in higher paid occupations, less for new entrants). And a somewhat lower threshold for “shortage occupations” and those with PhDs, especially in Stem subjects. This last will affect very few people but is presumably to placate Dominic Cummings. It is unclear if you’ll get even more extra points for being a misfit or a weirdo.

What will this mean for migration to the UK? Well, the government’s 90,000 figure was just wrong, and it’s notable that it hasn’t repeated it. Not because it wasn’t once a reasonable estimate of the impact of ending free movement – but because most of this impact has already happened. There aren’t 90,000 unskilled EU migrants coming here now. In fact, net migration from the EU may already be close to zero (we’ll get new figures next week). Moreover, the new system will be significantly less restrictive for migrants from outside the EU – whose numbers have already risen just as EU migration as fallen. So the overall impact on numbers is uncertain. In earlier work I estimated that a system like this might reduce migration by perhaps 40,000 a year, but the impact could well be even less. The government claims that overall numbers will indeed fall – and it might be right – but it’s far from certain.

That doesn’t mean some sectors won’t face challenges. Crucially it looks like the NHS and schools will be able to recruit skilled workers without worrying about salary thresholds (the national pay scales will apply). And finance, business services and higher education should also be able to live with this. But social care faces a big hit, unless it gets a big infusion of much-needed government funding that will allow it to increase wages and training budgets. Other sectors that have come to rely on EU migrants to provide a flexible (and often motivated and trained) workforce, from food processing to construction, will also be very worried.

But perhaps the most important unknown is delivery. If the government delivers on its promises to make the new system quicker, more efficient, less bureaucratic and more user-friendly, it could indeed be good news for employers and the wider economy. A more liberal system for skilled migration, from anywhere in the world, could genuinely help mitigate some of the economic downsides that are likely to result from the new trade barriers Brexit will bring from January.

That is a very big if. The Home Office already has a lot on its plate – implementing the settled status scheme for EU nationals who are resident here now, dealing with the ongoing fallout of the Windrush scandal, and so on. Its record hardly inspires confidence. And now it is being asked to introduce a new immigration system, to be up and running by the autumn of this year for people starting jobs from next January.

So there is a big opportunity here for the government, but also huge risks. With public opinion much more favourable to skilled immigration than free movement – but also much less worried about numbers or impacts than at the time of the referendum – it has a chance to put in place a system that enables people from all over the world to come here to live, work and contribute. That would go a long way to showing the world that post-Brexit Britain can genuinely be global. But if the introduction of the new system is rushed or bungled, then it will have failed in its first big test, and the rest of the world will notice. The pressure is now on.

• Jonathan Portes is professor of economics and public policy at King’s College London and a former senior civil servant