The number of calls to 999 - meant for use only in an emergency or when there is a threat to life - was up 14 per cent last month compared to June 2017.
And although New Year's Eve is traditionally the busiest day for the force's customer contact centre, this has been topped in the last week.
Calls levels have been regularly approaching record levels this month, the force revealed today.
On July 7 - the same day as England's game against Sweden and protests in Leeds and Wakefield - there were 2,307 calls to 999.
The number of calls was nearly 39 per cent higher than those received on New Year's Eve.
Customer Contact Centre Manager Tom Donohoe said: “Like many other police forces we have seen an increase in emergency calls with an unprecedented and sustained demand placed on call handlers.
“Despite this demand we have not abandoned a single 999 call over the past 12 months, something I am very proud of.
“We are doing what we can to ensure this demand is appropriately managed – including taking on more call handlers – but we also need the public’s help.
“We need callers to understand the demand we are facing. If a caller needs us in an emergency situation then we will get to you quickly."
Mr Donohoe it was right to prioritise calls from people facing a genuine emergency.
“I would ask members of the public to think which of the two scenarios they would prioritise first – a missing three year old child or a call for an update to a crime," he said.
“I would hope that everyone would think the missing child would be a higher priority, but if we are dealing with a missing child then that that means that the person calling for an update might just have to wait that bit longer."
He urged people seeking an update on a crime to think before calling either 999 or the more appropriate 101 non-emergency number when other options were available.
“It might be that your query can be resolved by having a look at our website or the Ask the Police site. Alternatively you can use our on-line facilities which includes a way of reporting crime on line and a web chat facility which is ideal forum for quick queries," he said.
“By doing so you can help us free up capacity to deal with the demand, so that people who are facing an emergency situation can get the help they so urgently need.”