Effective range theory, taking into account the polarisation interaction, is used for the extrapolation of the phaseshifts for the scattering of electrons by heavy alkali atoms to the region of thermal energies. The phaseshifts obtained are used for the calculation of impact broadening and the shift of Rydberg levels by alkali perturbers in the ground state. The parameters of the theory obtained from the ab initio calculations give a good description of the data on broadening and shift in the case of K and Rb. In the case of Cs the parameters have to be somewhat modified to give an agreement with experiment. The phaseshifts are also used for the calculation of the width and shift in the free-electron spin-resonance frequency due to collisions with heavy alkali atoms. The results of calculations are in good agreement with experimental data. The results for total and momentum transfer cross sections for the scattering of electrons with energies from 10^-4 to 10^-1 eV by K, Rb and Cs atoms are presented.