Job vacancies are at a record high, rising to 1.1 million in the three months to September.
The Office for National Statistics (ONS) also said the number of employees on payrolls has increased by 207,000 to 29.2 million.
It estimates the UK unemployment rate to be 4.5%, compared to 4% before the pandemic.
According to the ONS, there were 1,102,000 job vacancies in the three-month period between July to September 2021 - 3.7 empty posts for every 100 employee jobs.
A record number of vacancies were recorded across 12 of the ONS's 18 job categories.
The health sector had the most vacancies between July and September with 172,00.
The King's Fund think tank says the NHS is facing a "workforce crisis".
According to the latest annual State of the Adult Social Care Sector and Workforce in England report, the sector is struggling to recruit and retain staff, with more unfilled posts now than at the start of the pandemic.
The government says extra funding and a regular recruitment drive will help boost the workforce.
The hospitality sector had 134,000 unfilled roles. Many businesses say they're struggling to find staff, with some restaurants reducing their opening hours.
Industry bodies say one in five workers left the sector during the pandemic, with Brexit also blamed.
In addition, disruption to college courses as a result of Covid has interrupted the supply of new talent.
Retail and transport
There were 90,000 vacancies in retail, up from 65,000 in the previous quarter (April to June).
What effect did furlough have?
These figures cover the period when the government's furlough scheme came to an end.
It supported about 11.6 million jobs, with the majority of those in travel, retail and hospitality.
About one million workers were thought to be on furlough when the scheme ended last month, but the wave of job cuts some experts predicted doesn't seem to have happened.
Many businesses with large numbers of furloughed workers say they have taken everyone back. The number of redundancies proposed by employers in September was close to record lows, and unions say they're not aware of major job cuts.
How do I look for a job in this market?
Jobseekers should be ''strategic'' and target sectors experiencing shortages as well as those that are growing, says Gerwyn Davies, from human resources body the CIPD.
The shortage occupation list - used to offer work visas to people moving to the UK - shows where workers are needed. It includes fields like engineering, web programming and graphic design.
Consider your core skills, rather than hunting for a specific job title, suggests Corinne Mills, managing director of Personal Career Management.
For example, if you work in retail customer service, this could translate to other people-facing roles, such as sales.
How can I find out who is recruiting?
Many companies list jobs on their own website, or on recruitment sites.
You can also sign up with a general or specialist recruitment agency.
If you want to work for a particular company, check if it hires directly, or through a recruiter.
And if you want a specific job, be proactive and contact someone doing that role to discover how they got there.
Professional networks can also be useful. These could be LinkedIn or Facebook groups, or industry organisations, where jobs and events are posted and advice is available.
Some industries and employers have set up virtual networking events and job fairs.
How can I stand out from other applicants?
Corinne Mills suggests drawing on your personal network. Friends, family and acquaintances will collectively know hundreds of people, many of whom will be hiring.
Employers often respond to personal recommendations, and you may hear about roles before they are advertised.
Tech recruiter Amy Golding also recommends:
- Tailoring your CV and cover letter for each application
- Emphasising your skills and listing specific achievements such as finishing a project on time and within budget
- Showing enthusiasm and giving reasons why you want to do this job for this employer
- Proofreading your materials, including asking someone else to check them for spelling or grammatical errors which could mean your application goes straight in the bin