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David Cameron says he wants the UK to remain in the EU, but is trying to renegotiate British membership ahead of a referendumReuters

A little more than three years ago, David Cameron used a speech at Bloomberg to outline his priorities as he embarked on what was then the single-biggest challenge of his political career – a fundamental renegotiation of Britain's membership of the EU. Why? Because he promised voters a referendum on the country's EU membership to settle a debate that has raged for several decades.

He also promised to wrangle a new deal for the UK and has been hard at work since, schmoozing his way around the other 27 member states to eke out a number of policy changes that could convince, as Cameron would seemingly like to happen, British voters to stay in the EU. Now the EU Council president Donald Tusk has published the draft proposals for that deal – the 'Decision of the Heads' – which is yet to be agreed on by all the member states. These proposals may yet be revised and refined. But as it is, how does it stand up to Cameron's three original priorities set out in 2013?

One: Protecting the single market

Britain is not in the single currency, and we're not going to be. But we all need the eurozone to have the right governance and structures to secure a successful currency for the long term. And those of us outside the eurozone also need certain safeguards to ensure, for example, that our access to the single market is not in any way compromised.

What Cameron is getting at is that he wants clarity over a phrase in the 1957 Treaty of Rome on which the EU was founded. The Rome treaty commits members to "ever-closer union" with a view to becoming a federalised super-state. But the UK wants free trade, not ever-closer union. Tusk's deal goes some way on this. It sets out clearly that there exists a legitimate difference between those member states wanting to deepen integration and those that do not, such as the UK. The deal reinforces Britain's existing opt-outs under past treaties, such as staying out of the euro and the Schengen zone, and makes clear it would not be obliged to integrate more, such as in a banking union, though it cannot stand in the way of others wishing to deepen ties.

"It is acknowledged that member states not participating in the further deepening of the economic and monetary union will not create obstacles to but facilitate such further deepening while this process will, conversely, respect the rights and competences of the non-participating member states," says the draft deal. "The Union institutions, together with the member states, will facilitate the coexistence between different perspectives within the single institutional framework ensuring both the effective operability of Union mechanisms and the equality of member states before the treaties."

Two: Boosting competitiveness

Taken as a whole, Europe's share of world output is projected to fall by almost a third in the next two decades. This is the competitiveness challenge – and much of our weakness in meeting it is self-inflicted. Complex rules restricting our labour markets are not some naturally occurring phenomenon. Just as excessive regulation is not some external plague that's been visited on our businesses. These problems have been around too long. And the progress in dealing with them, far too slow.

One of the biggest criticisms of Europe is the bureaucracy, regulation and red-tape flowing from Brussels. Proponents argue this helps to protect product standards and workers' rights, among other things, but businesses say the rules are often pointless and needlessly burdensome. Cameron wants Europe to liberalise its rules and loosen its regulatory rigidity. Does Tusk's draft deal deliver on this? Not hugely. There are warm words about boosting competitiveness. But we have had warm words such as these before, and they soon cool when it comes to acting on them. "In these times of economic and social challenges, we need to breathe new life into the internal market and adapt it to keep pace with our changing environment," says the deal. "Europe must boost its international competitiveness across the board in services and products and in key areas such as energy and the digital single market."

Three: Returning sovereignty and improving democratic accountability

There is a growing frustration that the EU is seen as something that is done to people rather than acting on their behalf. And this is being intensified by the very solutions required to resolve the economic problems. People are increasingly frustrated that decisions taken further and further away from them mean their living standards are slashed through enforced austerity or their taxes are used to bail out governments on the other side of the continent.

There is little, if anything, on improving democratic accountability in Tusk's draft deal. Part of the frustration with the EU is it is seen as a haven for unelected bureaucrats and technocrats who, without democratic legitimacy, make rules that govern the lives of people in member states. Some of the criticism is overdone: the EU Council is made up of elected heads of governments and the EU Parliament is full of elected MEPs. Only the Commission is appointed, though its leaders are selected by elected politicians. But the Commission does have a lot of power and influence. And many in Britain feel it is unfair that politicians and technocrats from other countries can make laws under which they must live.

"On sovereignty, the proposed Decision of the Heads recognises that in light of the United Kingdom's special situation under the treaties, it is not committed to further political integration," reads Tusk's deal. "It also reinforces respect for subsidiarity, and I propose that the member states discontinue the consideration of a draft legislative act where a number of national parliaments object to it on the grounds of subsidiarity, unless the concerns raised can be accommodated." Subsidiarity in essence means letting national and local governments make laws and rules wherever possible, and the EU only intervening where it is necessary or more effective to. Some critics would argue the EU is never more effective than local and national governments, and has no right to intervene over their heads. Tusk is trying to reconcile the UK's demand for more sovereignty with the wider EU's desire for more integration.

What weakens his deal is that draft EU legislation will only be abandoned "where a number of national parliaments object to it on the grounds of subsidiarity". The exact number is vague, but we can be sure about this: if the UK is a lone objector, then tough. The draft legislation will continue.

What Cameron did not say in 2013

Nowhere in his Bloomberg speech does Cameron mention migration, despite this being the biggest issue that Britons have about the EU: the free movement of labour. There has been a large number of EU migrants entering the UK since the turn of the century. Some Britons are uncomfortable with the pace of immigration. Net migration is in the hundreds of thousands. But free-moving labour is a pillar of the EU, and other member states refused to consider scrapping this principle. As a compromise, Cameron has sought to restrict access to benefits for migrants, and some member states, including Germany, are open to this. What Cameron wanted was to stop EU migrants claiming working tax credits – an in-work benefit for those in low-paying jobs. This would, he hoped, deter some migrants from coming to the country and help him, as he had promised voters, to cut immigration numbers.

But many EU member states refused on the grounds that it would unfairly discriminate against their citizens. Instead, what has been offered in Tusk's deal is an "emergency brake" on paying benefits to migrants. If there is a sudden spike in migration to the UK, which puts a big strain on public finances, the government can request to use this emergency brake – officially called the "safeguard mechanism" to stop paying migrants benefits. "The European Commission considers that the kind of information provided to it by the United Kingdom shows the type of exceptional situation that the proposed safeguard mechanism is intended to cover exists in the United Kingdom today," says Tusk's deal.

"Accordingly, the United Kingdom would be justified in triggering the mechanism in the full expectation of obtaining approval." Critics say this is not good enough because it still demands that the UK asks permission from other EU member states to use this brake, so ultimately means that the country does not have control over its own welfare policy.

Will all of this be enough? Probably not. But it is only a draft, and is liable to change. Negotiations continue. Will Cameron get what he wants, and will it convince British voters to stay in the EU when the referendum takes place – potentially as soon as June 2016?