  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 E$_9$
exceptional field theory. The application to the reduction of D=11 supergravity
on $S^8\times S^1$ to SO(9) gauged supergravity is presented in a companion
paper.
