Federated Learning is a novel method of training machine learning models, pioneered by Google, aimed for use on smartphones. In contrast to traditional machine learning, where data is centralised and brought to the model, Federated Learning involves the algorithm being brought to the data, ensuring privacy is preserved. This paper will demonstrate how insurance companies in a market could use this technique to build a claims frequency neural network prediction model collectively by combining and using all of their customer data, without actually sharing or compromising any sensitive information with each other. A simulated car insurance market with 10 players was created using the freMTPL2freq dataset. It was found that if all insurers were permitted to share their confidential data with each other, they could collectively build a model that achieved 5.57% of exposure weighted Poisson Deviance Explained (% PDE) on an unseen sample. However, if they are not permitted to share their customer data, none of them can achieve more than 3.82% exposure weighted PDE on the same unseen sample. With Federated Learning, they can retain all of their customer data privately and construct a model that achieves a similar level of accuracy to that achieved by centralising all the data for model training, reaching 5.34% exposure weighted PDE on the same unseen sample.