Criminals will profit from a no-deal Brexit as they take advantage of shortages of food and medicine, according to one of Britain’s biggest police forces.

Gangs could exploit the demand for scarce drugs from worried patients and create hidden markets for goods held up at ports, an official report warns. Shoplifting and theft could also soar if people fear shelves becoming empty, leading to riots across the country.

But police chiefs are concerned that in the worst-case scenario they may not be able to get enough trained officers on the streets to tackle the disorder – because so many now refuse to give their personal phone numbers to bosses.

The most detailed picture yet of the impact on law and order of Britain crashing out of the European Union has been provided by Thames Valley police, the three-county force that covers Theresa May’s constituency as well as Boris Johnson’s Chequers retreat.

It comes after the government was forced to publish its assessment of the risks of a no-deal Brexit, known as the Operation Yellowhammer document, which reveals that food prices could rise and medical supplies run short because of huge hold-ups in cross-Channel trade.

The Thames Valley police report, published over the summer, states: “In a ‘worst case’ scenario, it is thought that crime not directly related to Brexit may rise in the event of a ‘no‐deal’ situation, due to the restricted availability of goods.

“Acquisitive crime will increase if the country faces shortages on food, fuel and medicines, this in turn could lead to widespread protest and disorder.

“Criminals may identify opportunities during times of uncertainty, issues with the ‘stockpiling’ of medicines may create a market for criminals to exploit as concerns grow over the availability of certain drugs making them a scarce commodity.

“In the wider spectrum, any shortage created by clogged trade routes shortages could provide opportunities for criminals to benefit.”

Even if Britain leaves the EU with a deal, the annual force management statement warns, “the repercussions of Brexit may create opportunities for OCGs [organised criminal gangs]. People trafficking, in particular may increase, as limits on legal immigration create demands for labour.”

Police chiefs have been preparing contingency plans for mobilising large numbers of public order-trained officers to take to the streets in the event of mass protests or riots after Brexit.

But the Thames Valley report admits: “There is some local concern about the ability to mobilise all specialist assets due to increasing numbers of officers who decline to provide personal contact information.

“This is an area of focus for the forces in view of the potential threat of national mobilisation being required in response to the EU exit.”

It also highlights the dangers of UK forces losing access to Europe-wide databases of wanted criminals as well as the power to extradite suspects easily.

“Public safety could be compromised if EU law enforcement agreements such as the European arrest warrant are no longer available post‐Brexit, and could result in a significant loss of operational capability.

“The loss of intelligence and enforcement co‐operation held with the EU could significantly hinder the ability to tackle some of the most prolific and serious offenders.

“Additionally the requirement to develop new processes to compensate for these changes may also create additional new ‘bureaucracy’ which has the potential to impact on capacity.”

The shadow policing minister Louise Haigh said: “This should act as an incredibly stark warning for the government and for the public of the risks of a no-deal Brexit.

“Not only do we not have enough police to cover the disruption that crashing out of the EU will inevitably create but it is now apparent we may see general crime rising thanks to shortages.

“Our police are already stretched to breaking point and leaving the EU without a deal would be deeply irresponsible for public safety and the resilience of our police and indeed society.”