A combination of flexible moulds as external formwork and bespoke robotically fabricated fibre reinforced polymer cages as tensile reinforcement offers a new opportunity for the manufacture of structural concrete components that have been optimised to minimise material use. This technology could potentially help in our quest to reduce carbon emissions in the construction industry, yet there remain technical issues to overcome if such flexibly formed concrete structures are to become a reality. This paper presents experimental research on fabric-formed T beams reinforced with Wound Fibre-Reinforced Polymer (W-FRP) to quantify the shear contribution of this novel system. It is shown that, depending on the geometry of the beam, carefully chosen flexural and shear reinforcement can resist shear in a predictable manner. Because of geometric variation along the length of the beam, shear resistance is found to move from being provided by both the W-FRP reinforcement and the sloping longitudinal reinforcement to being provided predominantly by the longitudinal FRP reinforcement as the W-FRP gradually ruptures. In turn, this demands higher anchorage capacity of the longitudinal bars than that might have been expected by design codes of practice. By overcoming such issues, this paper shows that savings in concrete of up to 64% can be made in the webs in such structures, compared with conventional T-beams.