Lord Sainsbury's Review of Science said there was a danger of a "race to the bottom", unless British firms moved into high value goods and services.
The UK had a good science record but needed to boost it quickly, he added.
Ministers responded by saying teachers who retrained as science specialists would be given an extra £5,000.
The government-commissioned report called for a major campaign to address the shortages of specialist science teachers.
It also wants to see more careers advice for those taking science, technology, engineering and mathematics (Stem) subjects in schools.
It said demand for graduates in these subjects was set to grow.
Although there was a reasonable stock of Stem graduates, potential problems lay ahead.
This was partly due to the 20-year decline in the number of pupils taking A-level physics, for example, it said.
Teachers should be given financial incentives and newly qualified teachers should be mentored.
Meanwhile the government should continue its drive to increase the number of young people studying biology, chemistry and physics separately.
Ministers should also consider giving all pupils the right to study a new further maths GCSE.
