The Bi2+xSr2-xCuO6+° (Bi-2201) phases and La substituted Bi-2201 compounds with general formulas Bi2Sr2-xLaxCuO6+δ and Bi2.3-xSr1.7LaxCuO6+δ were prepared and characterized by X-ray powder diffraction, electron diffraction, iodometric titration and resistance measurements. The monophasic samples of Bi2+xSr2-xCuO6+δ were obtained in air at 850°C for 0.15 ≤ x ≤ 0.4, while synthesis at 740°C in oxygen flow extended this range to the stoichiometric cation composition (0 ≤ x ≤ 0.4). The superconducting transitions were not detected for these monophasic samples in contrast to the La substituted phases which exhibited superconductivity, and the highest Tc,onset = 33 K was found for the Bi2Sr1.6La0.4Cu6.33 compound. Superconductivity in the Bi2Sr2-xLaxCuO6+δ series exists in overdoped and underdoped regions. Incommensurately modulated structures of nonsuperconducting Bi2.3Sr1.7CuO6.23 phase and superconducting Bi2Sr1.7La0.3CuO6.28 phase (Tc,onset = 26 K) were refined from X-ray powder data by a Rietveld technique using the four-dimensional space group P:A2/a:-11. The maximal Cu displacements from the average position in the first structure was found to be sufficiently larger than in the latter one. The distorted structural arrangement of the (CuO2) layers in the Bi2.3Sr1.7CuO6.23 structure can be a reason for the suppression of superconductivity in this phase, while their less corrugated configuration in the La containing Bi-2201 structure leads to the existence of superconductivity.