according to this site, 20 millisevierts a year is the exposure they allow airline workers, over a 5-year period, with 50 milliseverts in the worst year.
A pregnant woman flying 100 hours between the U.S. and Britain would exceed the recommended yearly dose for a fetus.
“The limit for radiation workers in the United States is 50 millisieverts per year, but we try to keep them to less than 5 millisieverts per year.”
http://articles.cnn.com/2011-03-18/world/japan.nuclear.reactors_1_radiation-millisieverts-japan-s-nuclear?_s=PM:WORLD
From that same article:
“For work involving recovery and restoration in an emergency operation, the International Commission on Radiological Protection recommends no more than 50 millisieverts in any given year.”
Airline travel (exposure to external sources of radiation) does not compare with living in contaminated regions where you are likely to inhale and ingest radioactive isotopes in addition to receiving external exposure. Internal (ingestion, inhalation) is much more damaging and supplies a continuing dose from particles lodged in body tissues.
FWIW, I found a study of airline stewards that found 30% higher levels of breast cancer and about twice as much skin cancer for those attendants flying for several years and accumulating higher doses. http://kuneman.smokersclub.com/PDF/58000flightattendants.pdf
From the study, it’s not clear how other contaminants, say, dry cleaning of airline uniforms or exposure to cabin smoke (when smoking was still allowed in flight)or exposure to jet exhaust on the tarmac contributed to these rates. Also - sleep disruption resulting from red eye flight schedules could also contribute to breast cancer rates. But the data is in keeping with the general idea that higher doses of radiation result in higher rates of cancer - even if not at the rates of ‘twice the skin cancer rate’ or ‘30% higher breast cancer rate’.