Foods to avoid Salt or sodium. Salt, or specifically the sodium in salt, is a major contributor to high blood pressure and heart disease. Deli meat. Processed deli and lunch meats are often packed with sodium. Frozen pizza. Pickles. Canned soups. Canned tomato products. Sugar. Processed foods with trans or saturated fat. What's the best drink for high blood pressure? Some drinks can help lower your blood pressure, including: Skimmed milk. Low-fat dairy products like yogurt and skimmed milk can help lower high blood pressure. Tomato juice. Beet juice. Hibiscus tea. Pomegranate juice.