Schools are beginning the term with rising numbers of teacher vacancies, the leading specialist recruiters say.
September vacancies were up a quarter on two years ago, one company, Eteach, said. Another, TeachVac, saw a 15% rise over two years to the end of August.
Eteach boss Paul Howells said he had "never seen so many unfilled posts", while heads are said to be "moving heaven and Earth" to get enough staff.
The government says more teachers are entering the profession than leaving.
But it published figures a few days ago suggesting the target for recruiting trainee teachers for 2017 would be missed for the fifth year in a row.
As pupils return to class, the number of vacant teaching posts in the 7,000 schools in the UK with which Eteach works has risen to nearly 14,000 - up 24% on September 2015.
'Scramble for staff'
The increase on September 2016 was 9%, according to the Eteach figures.
Chief executive Paul Howells said as schools were starting the new academic year, thousands would be "scrambling for last-minute supply staff and paying agencies a premium for emergency cover during a period of tightened budgets".
He said: "In my 20 years of working with schools on teacher recruitment, I have never seen so many unfilled vacancies.
"Teaching is failing to attract enough graduates, and schools are struggling to hold on to their current teachers, creating a perfect storm of pressures."
The number of vacancies on TeachVac, the free teacher vacancy listing service, rose about 15% to 19,215 between January and the end of August 2017 compared with the same eight-month period in 2015.
'Permanent fix needed'
Association of School and College Leaders head Geoff Barton said: "Schools have moved heaven and Earth to put teachers in front of classes for the start of this academic year, and in many cases will be using stop-gap solutions to deliver courses.
"What we must have is a permanent fix.
"It is clear that we need a national strategy to address this issue as a matter of urgency, in which the government and the teaching profession work together to find solutions.
"We need to attract more people into the profession, and then we need to make sure that we keep them."
He said head teachers knew the key ingredient to maintaining and raising standards was "a ready supply of teachers".
"Instead, we have an ongoing recruitment crisis which means many have to use supply staff on a routine basis and non-specialist teachers for subjects like maths and physics."
A Department for Education spokesman said it was investing £1.3bn until 2020 to attract more people to become teachers.
He added: "These figures do not reflect the fact that the teacher vacancy rate in 2016 remained low - at 0.3%.
"The number of teachers entering our classrooms is outnumbering those who retire or leave, and there are now more teachers in our schools than ever before - 15,500 more since 2010."