The Cu-O monolayer Tl2Ba2CuO6±δ is known to be an overdoped cuprate and Tc is controlled by the oxygen off-stoechiometry parameter δ. Samples with Tc ranging from ∼ 40K to 92K for orthorhombic and tetragonal phases have been prepared and systematically investigated by magnetization and differential susceptibility measurements in the reversible regime. This allows the deduction of the in-plane London penetration depth λab. We show the evolution of λab with Tc which does not fall on the Uemura plot established for the underdoped high Tc superconductors.