A new Institute of Directors (IoD) survey of over 800 members found almost nine in 10 back the development of a joined-up plan - set to be published next week - and their top priority is the implementation of a long-term skills strategy, with three-quarters saying this is particularly important.
Nearly two-thirds said infrastructure improvements need to be high on the agenda, while 60 per cent want the government to buckle down on rolling out fast broadband.
Just four per cent said cash support for at-risk large firms was "very important". If a large firm is at risk of closure, the most popular option among business leaders was for ministers to provide funds to retrain workers facing unemployment.
James Sproule, director of policy at the Institute of Directors, said: "It is painful to watch established businesses fail, but the government should be very sceptical of its power to keep struggling companies going through cash payments."
He added: "Leaving the EU is not the only way in which the UK will change in the coming years. As more jobs are taken on by robots or algorithms, and our population ages, it is vital we think seriously about the future of skills and training."
The strategy must also focus on the physical infrastructure that businesses need to be competitive, not only transport, but also the broadband network, which many firms feel is too slow.
On balance, our members favour improvements to existing infrastructure, and that will often mean essential but unglamorous road and rail upgrades.
Last year, a study be the Centre for Economics and Business Research for Arcadis found that a one-month delay in the transport infrastructure pipeline means the UK economy will miss out on around £2bn of investment-related GDP over the next five years - equivalent to £48,425 for each minute of delay.
Rail was identified as the greatest cause of stalled or cancelled transport infrastructure spend - a one month delay could result in up to £4.2m being added to the total delivery cost of all rail projects for each extra day.