Hello @adamharrisuk,
To remove the button you have to go through the child theme.
To know how to create and activate the child theme please go through below given link:
https://wptravel.io/how-to-create-a-child-theme/
After activating the child theme in your child theme functions.php add below given code.
remove_action( 'woocommerce_after_shop_loop_item', 'woocommerce_template_loop_add_to_cart' );
remove_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_add_to_cart', 30 );
Hope this helps.
Regards!!