The potential for reducing the Cost of Electricity (CoE) by using High Temperature Superconductors (HTS)in the Toroidal Field (TF) coils of a fusion tokamak power plant has been investigated using a new HTS module in the PROCESS systems code. We report the CoE and the design of HTS tokamaks that have been optimised by minimising the major radius of the plasma. Potential future improvements in both the superconducting properties and the structural materials for TF coils operating at 4.8 K and 30 K are considered. Increasing the critical current density by a factor of 10 (with a commensurate reduction in costs kA - 1 m - 1 ) results in a CoE 4.4% less than equivalent tokamaks using current low temperature superconductors (LTS). If the yield strength of the TF casing material is increased by 40% to 1400 MPa, the CoE is further reduced by 3.4%. Implementing both improvements and operating the TF coils at4.8 K leads to CoE of 19.1 (10.1) D cent kW - 1 h - 1 for a 500 MW (1.5 GW) HTS reactor compared to 20.7(11.1) D cent kW - 1 h - 1 for an LTS reactor (2013 costs). Operating the HTS TF coils at 30 K with both improvements, gives a similar CoE for HTS and LTS tokamaks.