Paraguay is a landlocked country sandwiched between Argentina to the south and Brazil to the north, plus it’s got Bolivia to the north-west. A lot of Brits get Paraguay and Uruguay confused.
It’s a long way from the sea, but it is linked to the sea by river and, yes, the British Navy has been up there. We have also been in conflict with Paraguay, but not in Paraguayan waters, so as far as I know at the moment we haven’t really invaded Paraguay.
In 1845, during the British and French blockade of the Rio de la Plata, Commodore Charles Hotham was operating with a British and French convoy and, despite Argentine attacks, in the Fulton he made it all the way to Asuncion, the present-day capital of Paraguay. The aim was to recognise Paraguay, lure the country into the war on our side and sign a treaty. The Paraguyans didn’t quite see it our way and we had to make the long return journey, again under Argentine attacks.
Then, in 1859, there was the Canstatt Affair, which led to the Buzzard/Grappler Affair. A lot of affairs. The president of Paraguay had imprisoned a certain Santiago Canstatt among a group of people he had accused of plotting to kill him by shooting him in a theatre. This was some time before Abraham Lincoln took his unfortunate trip to the theatre. Canstatt was a British subject and we weren’t very happy about him being chucked in jail. So two ships, Buzzard and Grappler, were dispatched to seize the Tacuari, Paraguay’s only warship, when it left Buenos Aires. The attempt failed, but shots were fired and the Paraguyan president reluctantly released Canstatt. The naval events took place outside Paraguayan waters, but it’s an interesting story anyway.
During the Paraguayan War of 1864–70, the Royal Navy was back in Paraguayan waters, running the enemy blockade into Paraguay on a number of occasions in attempts to get British citizens out.