Abstract With over a third of the United Kingdom's greenhouse gas emissions, decarbonising heat is key to achieving the Government's net-zero target by 2050. Here, we simulate high renewable zero-emission energy system architectures with heat supply based on the major options of district heating, heat pumps, and electrolytic hydrogen boilers. We adopt a novel whole system modelling approach that combines meteorology-driven hourly simulations of demand and supply with storage, flexible technologies, and interconnections on the European scale. Our results show that systems with heat supply based on consumer or district heat pumps require about four times less electricity per unit of heat, with a heat cost about half of that from electrolytic hydrogen boilers. Furthermore, we compare trade-offs between investment in different infrastructure components. For example, we find that, compared to the reference scenario, increasing renewable capacity by 33%, or interconnections by 200%, can lower system storage capacity by up to 50%.