The image below is of a specimen collected from the Portishead-Clevedon area of Somerset now housed at the Bristol Museum. As JulPal mentioned the crystals do look like calcite, but to be sure you can try to scratch them with a steel nail or knife. If the steel scratches the crystal then it is likely calcite since steel is harder than calcite (calcite=3 & steel~4-5 on the Mohs hardness scale). The pointed crystal are sometime referred to as dog tooth calcite and have a scalenohedral form. To me, the fossil on the back of your specimen looks like a piece of a brachiopod shell.
Unfortunately this image isn't labelled, but scanning through those listed on the provided line I'm wondering if they aren't calling it a calcite mudstone (I39).