British (and English/Scottish, pre-Union) attacks on Spanish America before 1800, by century:

16th Century

• 1568 – Battle of San Juan de Ulúa: John Hawkins' fleet attacked at Veracruz, Mexico.
• 1572–73 – Drake at Nombre de Dios: Francis Drake raided the Panamanian port and captured a silver mule train.
• 1577–80 – Drake's circumnavigation: Raids on the Spanish Pacific coast (Valparaíso, Callao, and other ports in Chile and Peru).
• 1585–86 – Drake's West Indies voyage: Sacked Santo Domingo and Cartagena de Indias.
• 1586–88 – Cavendish's circumnavigation: Thomas Cavendish raided Pacific ports (including Guatulco, Mexico) and captured the Manila galleon.
• 1595 – Raleigh and Drake's final voyages: Walter Raleigh burned San José de Oruña (Trinidad); Drake attacked Nombre de Dios and Porto Bello and besieged San Juan, Puerto Rico, where he died (1596).

17th Century

• 1617–18 – Raleigh's El Dorado expedition: Attacked Santo Tomé de Guayana on the Orinoco; Raleigh executed on his return.
• 1655 – Capture of Jamaica: Penn and Venables failed against Santo Domingo, then seized Jamaica.
• 1662–63 – Mings' raids: Christopher Mings sacked Santiago de Cuba, then Campeche (with subsequent raids by other buccaneers, e.g., the 1685 sack of Campeche).
• 1668–71 – Morgan's raids: Henry Morgan took Puerto del Príncipe (Cuba), Portobelo, Maracaibo, and burned Panama City (1671).
• 1680s – Buccaneer raids: English buccaneers (Bartholomew Sharp, others) crossed Panama and raided Pacific settlements.
• 1698–1700 – Darien scheme: Scottish colonization attempt on the Panama coast (failed, not an attack per se).

18th Century

• 1708 – Wager's action: Charles Wager destroyed Spanish treasure ships off Cartagena de Indias.
• 1739–43 – War of Jenkins' Ear: Admiral Vernon captured Porto Bello (1739), failed before Cartagena (1741), and attacked Guantánamo, Cuba (1741); assaults on La Guaira and Puerto Cabello, Venezuela (1743). Anson's squadron also raided Paita, Peru (1742).
• 1762 – Capture of Havana: British seized Cuba's capital in the Seven Years' War (returned to Spain in 1763).
• 1797 – Abercromby's Caribbean campaign: Captured Trinidad (February); failed attack on San Juan, Puerto Rico (April).

Note: The British invasions of the Río de la Plata (Buenos Aires and Montevideo, 1806–07) fall just into the 19th century, so they're excluded from this list.