Flow cytometry is currently the gold standard for analysis of cells in the medical laboratory and biomedical research. Fuelled by the need of point-of-care diagnosis, a significant effort has been made to miniaturize and reduce cost of flow cytometers. However, despite recent advances, current microsystems remain less versatile and much slower than their large-scale counterparts. In this work, an all-silica fibre microflow cytometer is presented that measures fluorescence and scattering from particles and cells. It integrates cell transport in circular capillaries and light delivery by optical fibres. Single-stream cell focusing is performed by Elasto-inertial microfluidics to guarantee accurate and sensitive detection. The capability of this technique is extended to high flow rates (up to 800 μl/min), enabling a throughput of 2500 particles/s. The robust, portable and low-cost system described here could be the basis for a point-of-care flow cytometer with a performance comparable to commercial systems. © 2017 The Author(s).