A team of more than 300 police officers set up for incidents relating to Brexit has been "very heavily deployed and busy" since it started last week, Police Scotland have revealed.

The dedicated unit for Brexit-related emergencies has already been dispatched to deal with protests and "increasing febrile" behaviour in the streets, according to Police Scotland deputy chief constable Will Kerr.

Funding for the additional officers is a source of concern, with the force's budget revealed to be facing a large shortfall of the £17m needed.

The Scottish Government believes any costs related to Brexit should not impact on Scotland's public finances, and should be met by the UK Government in full.

Police bosses said the flexibility of the unit to respond to incidents across Scotland has already proved useful.

Speaking at a meeting of the Scottish Police Authority (SPA), Mr Kerr said the reserve force, made up of 300 officers and 12 public support units, started early on Monday, March 18, and has already been "heavily deployed and busy".

Mr Kerr said: "Last Friday alone there were three almost like flash protests at sites across Edinburgh, both March for Europe and a separate march at the Parliament.

"We were able to draw down very quickly on this with an additional, very mobile national asset and move them to that protest site as quickly as possible.

"We were also able to use the mobile reserve to police the Scottish Defence League march in Edinburgh on Saturday as well."

Addressing increased tensions following the EU referendum, both in public and on social media, he said: "We're seeing a lot of discussion becoming increasingly heated and so having that operational flexibility is going to be incredibly valuable over the next few weeks."

Protecting politicians from the potential wrath of disgruntled people was also cited as a key issue for police.

Mr Kerr said: "People have a right to protest lawfully and peacefully, and we will protect the right to do so, while making sure that politicians are allowed to go about their very important business over the next couple of weeks and months, with the full assurance and support of Police Scotland that they can do so safely.

"That is our increasing concern about the very febrile, some very aggressive, some very hostile comments that we have seen playing out on social media sites - making sure that doesn't translate to actual physical interaction and contact with our politicians as they go about their important business."

Extra policing costs in Scotland for Brexit fallout has been estimated at £17m but, in the SPA's papers for the board meeting, chief financial officer James Gray warned "there is insufficient funding in 2019-20 to deliver the business case in full", with a potential knock-on effect for officer numbers in the future.

Susan Deacon, the SPA chairwoman, said: "Policing is a very obvious area where there are very real cost implications of preparing for Brexit and I don't think anyone would question the absolute necessity for public safety to be the primary consideration through this period."

She added: "It is for the Scottish Government to address how and where it finds additional resources, whether it be within its own coffers or through negotiations with the UK Government but I think we have an absolute responsibility to be clear about what the impact on policing is."

During the board meeting, chief constable Iain Livingstone claimed that the investment in the force's fleet was most likely not sustainable beyond the next 12 months.

He stated that the force faced a challenge and would have to make a case for increased capital allowance by highlighting the return it would have for public safety, community cohesion and wellbeing.

Following the meeting, he told STV News: "They are working with IT equipment, they are working with and in buildings and estate that is dated, that are not fit for purpose for the 21st century.

"To build an organisation that's going to be sustainable, that's going to be efficient, that's going to be effective we need to make that level of investment.

"Now at the moment I am confident that there is no threat to public safety but I do think it's important that I highlight the need for that sustained investment."

James Gray, chief financial officer of Police Scotland, also highlighted his concerns.

He said: "The organisation is in a position of setting a budget where the spend on maintenance will be £9 per sq compared to a UK policing average of £38 and that's not to say others are spending the right amount of money but I'm highlighting the fact that this organisation will be setting a budget where maintenance is less than a quarter of the average for the UK in policing.

"And the amount of money being set aside for fleet works out at £1500 per vehicle. Now an average vehicle that's purchased for Police Scotland is £15,000 so what that tells you is if this was to continue, over time and into the longer term, then police vehicles would have to be retained for 10 years before they could be replaced.

"So I say that simply as this is something that will become more acute in the future...there is a question around sustainability of what's being done here that needs to be addressed into the future."

In response, a Scottish Government spokesperson said: "We are very clear that any costs related to Brexit should not impact on Scotland's public finances, and should be met by the UK Government in full.

"It is abundantly clear that Brexit is going to cost Scotland more than the consequentials delivered by Westminster.

"While the allocation of resources is for the chief constable and SPA to determine, we are protecting the police resource budget in real terms in every year of the current Parliament, delivering a boost of £100m by 2021.

"Total Scottish Government funding for the SPA in 2019-20 is increasing by £42.3m, bringing the annual policing budget to more than £1.2bn.

"This includes a 52% increase to the capital budget - providing £12m more - which will fund essential investment in IT infrastructure and support mobile working for officers, allowing them to access information remotely and spend more time in communities."