Measuring contact friction in soft-bodies usually requires a specialised physics bench and a tedious acquisition protocol. This makes the prospect of a purely non-invasive, video-based measurement technique particularly attractive. Previous works have shown that such a video-based estimation is feasible for material parameters using deep learning, but this has never been applied to the friction estimation problem which results in even more subtle visual variations. Because acquiring a large dataset for this problem is impractical, generating it from simulation is the obvious alternative. However, this requires the use of a frictional contact simulator whose results are not only visually plausible, but physically-correct enough to match observations made at the macroscopic scale. In this paper, which is an extended version of our former work A. H. Rasheed, V. Romero, F. Bertails-Descoubes, S. Wuhrer, J.-S. Franco, and A Lazarus, "Learning to measure the static friction coefficient in cloth contact," in Proc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit., 2020, pp. 9909-9918, we propose to our knowledge the first non-invasive measurement network and adjoining synthetic training dataset for estimating cloth friction at contact, for both cloth-hard body and cloth-cloth contacts. To this end we build a protocol for validating and calibrating a state-of-the-art frictional contact simulator, in order to produce a reliable dataset. We furthermore show that without our careful calibration procedure, the training fails to provide accurate estimation results on real data. We present extensive results on a large acquired test set of several hundred real video sequences of cloth in friction, which validates the proposed protocol and its accuracy.