Mathematics should be a compulsory subject for everyone aged 16 to 18 whether they are doing A-levels in humanities or training courses to become beauticians or plumbers, according to leading scientists.

A dire lack of mathematical understanding permeates all levels of society – and even science students who have maths A-level still find that they fall short of what is required when they enter university, experts found.

Lords Rees, the Astronomer Royal and master of Trinity College, Cambridge, told The Independent: "We need to ensure that fewer people are bewildered and bamboozled by numbers." Lord Winston, the television presenter and professor of science and society at Imperial College London, said that mathematics lies at the heart of rational decision making and everyone should aspire to understand its basic principles.

"Our economy increasingly needs people who are really well-trained in mathematics and science," he said. "Even some first-year undergraduates require remedial maths teaching for certain courses at several leading universities – even after taking A-level double maths successfully."

Britain continues to lag far behind other countries when it comes to maths education, even though the problems were identified more than a decade ago. In 2009, the UK came 28th in an international educational league table in maths based on the skills of 15-year-olds – well behind many European and east Asian countries.

Forcing all students over 16 to continue with mathematics would be one way of addressing a problem that is viewed as one of the greatest challenges to producing a generation of young people who can compete in the global knowledge economy. The House of Lords Select Committee on Science and Technology has recommended that drastic action be taken to promote a greater awareness and understanding of mathematics in schools.

Making maths compulsory beyond the age of 16 is one way of helping to solve the problem, it says.

"There is no doubt at all that we have a major problem with mathematics and we recommend that the Government should make it compulsory for maths to be studied in some form by all students over the age of 16," said Lord Willis, chairman of the Lords subcommittee on higher education, and a former Leeds headmaster. "When you've got the vice-chancellor of Cambridge University saying that 'We've got nothing but A* students coming in and yet we have to do remedial mathematics for them to engage in engineering and physics', there is something seriously wrong."

He said non-science students, whether taking A-levels in humanities or vocational training courses, would benefit from lessons in maths after the age of 16. "There is hardly any area that doesn't have mathematics to underpin it."

About 85 per cent of students in England give up maths at 16. Many A-level science students are dropping maths as early as they can, the Lords found. Leading scientists agree that making maths compulsory between 16 and 18 would help to compensate for the poor maths teaching in primary and secondary state schools. "We were absolutely gobsmacked to find that 20 per cent of engineering undergraduates, 38 per cent of chemistry and economics undergraduates and 70 per cent of biology undergraduates do not have A-level mathematics," Lord Willis said.

Lord Winston said maths teachers need to find more engaging way of teaching, while Lord Willis said: "Many commentators would say that mathematics teaching in our schools is really glorified numeracy."

Expert views: how to tackle the crisis

"So much of our lives is governed by science"

Dr Maggie Aderin-Pocock, physicist and television presenter:

"I am really heartened by this proposal. So many areas of our lives today are governed by maths and science, so having an awareness of these subjects is crucial in order to make the right decisions. Many younger students feel that maths is irrelevant to everyday life, so teaching the subject in an engaging and accessible way is vital.

"Obviously not everybody wants to be a mathematician or a scientist, but showing the relevance of these subjects is becoming increasingly important to all of us."

"Maths teaching needs to be much more exciting"

LORD (ROBERT) WINSTON, professor of science and society at Imperial College London:

"It is the basis for rational decision-making as well as the basis of all science. We live in a society that, to some extent is mathematically, as well as scientifically, illiterate. Yet our economy increasingly needs people who are really well-trained in mathematics and science.

"Maths teaching at all ages should be more exciting. It would engage the enthusiasm of more students. One way of involving them is to introduce mathematical concepts into all science and engineering practicals to make maths more relevant. Most schools are still not doing nearly enough practical and experimental science."

"We are out of line with the rest of Europe and Asia"

LORD (MARTIN) REES, Astronomer Royal, Master of Trinity College Cambridge:

"This country is very much out of line with others in the very low proportion of young people studying any kind of mathematics after the age of 16. Our secondary education system is weak compared to that of other nations in Europe and the Far East. Moreover, our system is over-specialised in its later stages.

"But we shouldn't just worry about those who go on to higher education. Everyone, whatever career they take up, needs to be at ease with quantitative reasoning. Not all will be suited to the same curriculum, but we need to ensure that fewer people are bewildered and bamboozled by numbers."

"Without extra money, how could it be introduced?"

Professor Stephen Sparks, chair of the Advisory Committee on Mathematics Education:

"We have been concerned for some time about the proportion of students who continue with mathematics after 16. Whether it should become compulsory depends on what courses exist, the availability of teachers and whether other subjects are also expected to be compulsory. Currently, the mathematics courses available will not meet the needs of all students.