There are a few baseball idioms you'll hear in the UK from time to time... Out of left field, three strike policy, a "home run" for a thing that was a great success, ballpark figure... None are extravagantly popular, but you do hear them. As to cricket - "smashed it out" is relevant, but no-one ever calls the playing area a park. You hit it over the boundary, or out of the ground, not over the fence or out of the park.

It’s actually a reference to how we throw our cucumber sandwiches out of the National Heritage park once all the tea has been drunk