I'd never heard of Branston pickle but needed a picnic sandwich for my vegetarian sister. This is really flavorful and we all loved it!! I found Branston pickle at a local British store by looking on the Internet. It's like a vegetable chutney in sauce (think A1 but not exactly).ranston Pickle and Cheese Sandwich. 5 5. I'm actually eating one of these as we speak. I'm watching my calorie intake, so I serve mine on reduced calorie multi-grain bread with a slice of extra sharp cheddar and some slices of raw onion.