Signalling network inference is a central problem in system biology. Previous studies investigate this problem by independently inferring local signalling networks and then linking them together via crosstalk. Since a cellular signalling system is in fact indivisible, this reductionistic approach may have an impact on the accuracy of the inference results. Preferably, a cell-scale signalling network should be inferred as a whole. However, the holistic approach suffers from three practical issues: scalability, measurement and overfitting. Here we make this approach feasible based on two key observations: 1) variations of concentrations are sparse due to separations of timescales; 2) several species can be measured together using cross-reactivity. We propose a method, CCELL, for cell-scale signalling network inference from time series generated by immunoprecipitation using Bayesian compressive sensing. A set of benchmark networks with varying numbers of time-variant species is used to demonstrate the effectiveness of our method. Instead of exhaustively measuring all individual species, high accuracy is achieved from relatively few measurements.