Welcome to Seaton Beach, where you are looking for one in a million (or probably even worse odds).
Stealth is required due to passing muggles, especially if the adjacent cafe is open during the summer. There's no need to search around the food hut. It's probably best to jump down onto the beach and to sit and search so as not to attract attention. Tweezers may be required to extract the log sheet. No dogs allowed on this section of the beach in the summer, when there's also a parking charge along Seaton Esplanade (free during the Winter months).
May the odds be ever in your favour