Uniform large deviation principles for positive functionals of all equivalent types of infinite-dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational representation formula, which for an infinite sequence of independent and identically distributed real Brownian motions and a Poisson random measure was shown in [A. Budhiraja, P. Dupuis and V. Maroulas, Variational representations for continuous time processes. Ann. Inst. H. Poincaré (to appear)].