The Alexandria Board of Equalization and Review has refused to lower the real estate tax assessment on the unsold condominium units owned by Union Bank of California at the Place One complex.

The bank had appealed the Alexandria real estate tax assessor's ruling that raised the assessment by $627,000 on the 175 unsold units owned by the bank. The board's decision means that Union Bank will have to pay an additional $10,659 in real estate taxes for 1977. At least some of his money, however, is expected to be prorated by the bank among the individuals who have purchased almost 100 units in the building since the assessment on Jan. 1, 1977, on which the tax is based.

Individual owners of condominiums at Place One, located at 5500 Holmes Run Pkwy, in Alexandria, also had their real estate tax assessments raised by the real estate tax assessors office last year. The owners appealed to the board but they, too, were turned down.

The practice of granting developers and banks who own large amounts of unsold units a real estate tax break but not to the individual condominium owners has raised an outcry among private owners of the units. The Alexandria real estate tax assessors' office says the practice is necessary to maintain a fair market value on the property as required by the Virginia Constitution.