Businesses, the NHS and schools would be in a “terrible position” if there was a large reduction in migration post Brexit, shadow home secretary Diane Abbott has claimed.

Ms Abbott said the Government should be listening to the concerns of the public sector amid fears of a “collapse” in the number of EU migrants moving to the UK.

Speaking on BBC One’s The Andrew Marr Show, she outlined Labour’s position was to have “less bureaucracy” to allow easy movement for EU migrants.

Ms Abbott said: “The health service, they’re very worried about a collapse in the number of EU migrants coming here.

“Social care would be in a terrible position, the health service, finance, education, so we will be listening – as the Government should be listening – to what business and the public sector says about its needs for labour.

“At this point, both business and public services like health and education are saying we do indeed need these eastern European migrants that are coming here.

“The reality is that business, the CBI, the Institute of Directors but also health, education and social care, they say that they need these European migrants and we have to listen to them.”

Asked to elaborate on shadow Brexit secretary Sir Keir Starmer’s call for easy movement, Ms Abbott said Labour would put in place a “fair and reasonable” system to manage migration.

She added: “We will have to see how this negotiation goes. It may involve a visa system, but we have to see how these negotiations the Government’s undertaking go.”

Meanwhile, Theresa May will today tell MPs the UK will seek to sign trade deals with other countries, despite potentially being bound by European Union rules for around two years after Brexit.

The Prime Minister will say that, despite leaving the single market and customs union, she wants “access to one another’s markets” to continue “as now” during an implementation period.

The EU’s guidelines say that, during any transition period, the UK would have to comply with the bloc’s trade policy, preventing it from striking its own deals with other countries.

But Mrs May will say the UK wants to sign agreements which would come into force after the “strictly time-limited” period has ended.

“We will prepare for our future independent trade policy by negotiating – and where possible signing – trade deals with third countries, which could come into force after the conclusion of the implementation period,” she will say as she updates the Commons on a Brussels summit which saw her 27 EU counterparts agree to move on to the next phase of Brexit talks.

Mrs May and her senior ministers will also begin the process of thrashing out the Government’s plans for a post-Brexit UK-EU trade deal as Brussels indicated she may not get the “special partnership” she wants.

A meeting of the Brexit “war cabinet” – formally called the Cabinet European Union Exit and Trade Committee – will take place today, with a full Cabinet tomorrow, as ministers formally consider the relationship the Government wants with the EU.

The Prime Minister will say there is a “shared desire” between the UK and EU for “rapid progress on an implementation period” before any UK-EU deal comes fully into effect.

The EU’s negotiating position makes clear the bloc expects the UK to observe all of its rules – including on freedom of movement – and accept the jurisdiction of the European Court of Justice (ECJ) during this time.

Mrs May will say “during this strictly time-limited implementation period which we will now begin to negotiate, we would not be in the single market or the customs union, as we will have left the European Union.

“But we would propose that our access to one another’s markets would continue as now, while we prepare and implement the new processes and new systems that will underpin our future partnership”.

Indicating that free movement rules will not continue in exactly the same way, she will say that “during this period we intend to register new arrivals from the EU as preparation for our future immigration system”.