We develop in detail the general framework of consistent Kaluza-Klein truncations from D=11 and type II supergravities to gauged maximal supergravities in two dimensions. In particular, we unveil the complete bosonic dynamics of all gauged maximal supergravities that admit a geometric uplift. Our construction relies on generalised Scherk-Schwarz reductions of E9 exceptional field theory. The application to the reduction of D=11 supergravity on S8 × S1 to SO(9) gauged supergravity is presented in a companion paper.