Crystal and magnetic structures of the high-pressure stabilized perovskite phase of TlMnO3 have been studied by neutron powder diffraction. The crystal structure involves two types of primary structural distortions: a+b-b-octahedral tilting and antiferrodistortive type of orbital ordering, whose common action reduces the symmetry down to triclinic P -1. The orbital pattern and the way it is combined with the octahedral tilting are different from the family of LnMnO3 (Ln = lanthanide or Y) manganites who share with TlMnO3 the same tilting scheme. The experimentally determined magnetic structure with the k = (1/2,0,1/2) propagation vector and P_S-1 symmetry implies anisotropic exchange interactions with a ferromagnetic coupling within the (1,0,-1) planes and an antiferromagnetic one between them (A type). The spins in the primary magnetic mode were found to be confined close to the (1,0,-1) plane, which underlines the predominant role of the single ion anisotropy with the local easy axes of Mn3+ following the Jahn-Teller distortions of the octahedra. In spite of the same octahedral tilting scheme in the perovskite structures of both LnMnO3 and TlMnO3 manganites, a coupling of the secondary ferromagnetic component to the primary A-type spin configuration through antisymmetric exchange interaction is allowed in the former and forbidden in the latter cases.