Deaths from mesothelioma are expected to peak between 2015 and 2020, according to a report in the British Medical Journal.
It said that as exposure to asbestos in the UK continued until 1980, "the peak of the epidemic is still to come".
At its peak, mesothelioma is expected to cause 2,000 deaths a year in the UK, up from current levels of 1,800.
Construction workers' union UCATT has warned that the situation will become worse if calls for a relaxation in the restrictions on the use of asbestos are heeded.
UCATT general secretary George Brumwell said: "We hear increasing calls for relaxation from some Tory MPs and of course from the asbestos industry.
"If that were to happen the epidemic which the British Medical Journal is predicting will be much worse than doctors fear."
UCATT said that up to 500,000 UK workplaces still contained asbestos.