We have measured the thermopower and resistivity of two series of cuprate superconductor, TI,.,Pb,,,Sr,_,La,CuO~ and Bi,Sr,-,LaxCuO,+, , which possess a single CuO, plane. In each series, the hole concentration can be varied by changing the La content, permitting investigation of the overdoped, maximum-T, and underdoped regimes. The thermopower follows a pattern similar to that seen in superconductor series with more than one CuO, plane, namely an approximately linear decrease as temperature increases well above T,. However, the thermopower shows a minimum above T, followed by a maximum as temperature increases for samples with a small thermopower and high T,. The magnitude of thermopower as a function of To is in general agreement with the universal behaviour found for other cuprate superconductors.