Yesterday - Friday - saw the force receive a record total of 5,432 telephone calls from the public, of which 1,789 were emergency 999 calls.
On a normal busy day, call handlers can expect to field around 1,000 such calls, the force said.
The spike in calls is an emerging trend, with the force highlighting how, since January, it has taken 27,000 more calls than during the same period in 2015. The majority of this increase has occurred since April and the warm weather of the past two weeks has seen calls rise to new peaks, said assistant chief constable Mark Milsom.
He said: “The present high demand we are receiving is placing great pressure on our services and our staff are doing everything they can to answer the telephones and attend incidents.
“And it isn’t simply about numbers and statistics. Of the 65 people that are daily reported missing to us, many are young and vulnerable. By way of example, yesterday, two girls aged 14 and 15 went missing from their care home and were known to be at high risk of sexual exploitation. Extensive enquires involving multiple officers finally traced and returned them both safely. Between them both girls have been reported missing on 14 occasions over the last fortnight.
“We are therefore prioritising calls where safety is at risk such as missing persons and emergency calls - and by doing so we were able to answer yesterdays 999 calls in 12 seconds, on average.
“Unfortunately this prioritising has meant that other services such as 101 calls have taken us longer than normal. We do apologise for this and will be working hard over the next few days to clear any backlogs.”