There has been a lot of debate recently about what being a member of the single market requires in terms of freedom of movement. People on all sides of the debate say that staying in the trading bloc means accepting unfettered freedom of movement – but the reality is more complex than that.

David Cameron’s botched renegotiation before the referendum reinforces this view, because at the same time it failed to reassure those with concerns and also alarmed those who wanted a fair system to manage migration. He satisfied no-one, and ultimately failed to convince the British public.

It’s clear that many people voted for Brexit because they wanted more control on immigration. This may not necessarily mean just cutting the numbers, and many people welcome the vital work that migrants do, and the contribution they make to our communities and the economy. But pro-Brexit politicians often suggest schemes to allow continued high levels of migration for workers in sectors such as agriculture, hospitality and distribution which could just perpetuate existing exploitation and undercutting.

However, often missed in the debate about freedom of movement is this: the UK could exert greater control over immigration through creative means that don’t require leaving the single market. It is open to any UK government to implement domestic policies to reduce the impact of immigration. And, in our negotiations as we leave the EU, we could choose to follow the precedents set by a number of countries who are inside the single market but nonetheless have tighter policies than unfettered freedom of movement.

Firstly, this government could do much more to manage the impact of migration and allay concerns about undercutting and pressure on public services. All of these actions are open to any UK government – and don’t require leaving the single market. The government could invest in enforcement of workers’ rights and the national minimum wage and make sure that agency workers and “posted” workers couldn’t be used to undercut local labour markets. They could prohibit agencies from recruiting solely outside the UK. And they could enable unions to go into every workplace to stop exploitation.

To deal with concerns about pressure on public services, the government should abandon underfunding of schools and hospitals, crack down on rogue landlords and start a building programme for the council houses the UK needs. These policies would reduce the competition between existing residents and new arrivals which has done such harm to community relations.

Secondly, the government could follow the lead of other European countries which are in the single market but which have chosen to exercise more control over migration than the UK currently does. By definition, these interpretations of freedom of movement do not require leaving the single market – but do represent meaningful controls. The examples show that far from a dogmatic insistence on one form of freedom of movement, there are a range of options available inside the single market.

Examples of the policies that other countries inside the single market have adopted include:

Restricting public sector jobs to nationals only

Requiring migrants planning to stay longer than a few months to register upon entry with the relevant local authority

Requiring all vacancies in sectors where unemployment is above average to be published with the government’s own employment service, with applications allowed only from those unemployed people already registered with the service

Negotiating arrangements to limit the number of European Economic Area nationals entering the country (the equivalent of limiting the number of national insurance numbers issued)

Not all of these specific measures would meet the UK’s needs – and nor would they all get TUC approval. But they show what can already be done while remaining in the single market – and they demonstrate that the EU migration model that the UK has chosen up until now is not the only model on offer.

These two strategies, taken together, would represent a significant extension of domestic control over migration from the EU. And they would allow the UK to respond to voters’ concerns, expressed in the Brexit vote, whilst not closing off the option of continued single market membership.

At this stage, keeping our options open is the best way forward as we seek a Brexit deal that delivers for working people. Remaining in the single market seems the best way to protect jobs and workers’ rights into the future, but all possibilities should be considered.

Owen Tudor is head of EU and international relations at the TUC.