Newham, in east London, could be the first borough to introduce the new terms, which would be in place by September next year if parents and teachers agree. Under the Newham scheme, the six-week summer holiday would be cut to four. Children would also have four two-week holidays in October, December, March and May.
Ian Harrison, Newham's director of education, said: "We agree with the Government that there appear to be certain advantages with a five-term year. The autumn term is extremely long at the moment and the summer break is very big, which may be good for staff but may not be so good for pupils."
Croydon council, in south London, will put similar proposals to parents next term, and could introduce the new system in 2001. Officials at Thurrock council, Essex, are also considering the change.
Education officials said equal-length terms would cut truancy, raise standards and help stop parents taking term-time holidays.
Teachers' unions condemned the proposals and parents warned that they may prove unworkable.
Margaret Morrissey, spokeswoman for the National Association of Parent Teacher Associations, said: "A lot of working parents would welcome more evenly spread holidays, but people do like the long summer break. There could also be very great problems for people who need to make childcare arrangements."