For those interested in the history of exploration, what is there to see in London?
The Hakluyt Society has its postal address in the map room of the British Library at St Pancras. They have one or two lectures a year dealing in the history of exploration and publish dozens of journals from the golden age of exploration.
The British Library also contains many original manuscripts (journals, logbooks, letters, books) from various voyages including Cook, Flinders, Harriot, Vancouver, etc. These have to be requested in the Manuscripts room. Occasionally the journals of Scott and Cook are placed on display in the treasures exhibition in the John Ritblat Gallery. The journal of Samuel Wallis, discoverer of Tahiti, is at the National Archives at Kew. Many publications recounting voyages that were popular in their day are now out of print. An example is William Dampier's New Voyage Round the World 1697.
There is a Captain Cook Society, but it is not based in London, having meetings up in Yorkshire and in Australia. Besides the Hakluyt Society and James Caird Society, there don't seem to be any other societies based in London relating to explorers or the history of exploration. The far future of exploration i.e. space travel, is covered by the British Interplanetary Society.
The British Museum in Bloomsbury has a few rooms containing objects collected by explorers. The Enlightenment Gallery (Room 1) on the ground floor has objects from Australasia and Polynesia collected by Captain Cook as well as some shells collected by William Dampier. There are also engravings and copper plates from Joseph Banks' Florilegium. North American objects collected on Cook's third voyage (late 1770s) are in with the North American collections, curated by Jonathan King. In Room 46 (upstairs), there are also some cameos to Cook and Banks, as well as Cook's Copley Medal (for tackling scurvy) and a Wedgwood medallion made from clay brought back by Captain Arthur Philip from Sydney Harbour.
The National Maritime Museum at Greenwich has the Oceans of Discovery gallery showcasing objects, maps and journeys from the age of discovery e.g. Cook's journals, a model of the Endeavour, and navigational instruments. There is also a display dedicated to Antarctica. Next door in the Queens House (designed by Inigo Jones) is a gallery dedicated to William Hodges' landscapes and portraits from Cook's second voyage. There is also a portrait to Lord Sandwich, one of Cook's patrons. Up on the hill is the famous Royal Observatory. In its museum are the Kendall marine chronometer copies of Harrison's H4 that sailed with Cook, Bligh and Flinders. There's also a logbook from Anson's 1740-44 voyage. Edmund Halley, who conducted his own voyage to the south seas, is commemorated by a portrait and a tombstone at the entrance to Flamsteed's house. The library of the National Maritime Museum has moved into a new building in 2011 and houses extensive maps, journals, logbooks, ship blue prints, admiralty reports, and other publications relating to the history of exploration. Anyone can be a member and explore the manuscripts and books in the reading room.
The Royal Society, which sponsored some voyages of exploration, such as Cook's Endeavour voyage of 1768-1771 has various records from its on-board naturalists and scientists. It's located at Carlton Terrace and has a lending library.
Portraits: Portraits of ship's captains can be found at Greenwich and in the National Portrait Gallery. At Greenwich, the famous Dance portrait of Captain Cook is normally on display in the National Maritime Museum, as is one of James Clark Ross. At the National Portrait Gallery, Francis Drake, Walter Rayleigh, William Dampier and Joseph Banks can usually be seen as well as a Cook engraving.
Statues: Captain Cook is commemorated with statues at Greenwich and at The Mall just west of Admiralty Arch (near Trafalgar Square). At Waterloo Place near the Royal Society are statues to John Franklin and Robert Falcon Scott. A statue of Joseph Banks is in the Natural History Museum at Kensington (upstairs near the sequoia).
Blue plaques: In Greater London there are plaques to Captain Cook (Mile End), Matthew Flinders (Fitzroy Square), Robert Fitzroy (Onslow Square), James Clark Ross (Blackheath), and Robert Falcon Scott (Oakley Street Chelsea). William Bligh's old house is on 100 Lambeth Road (close to the Imperial War Museum), near where he is buried in the Museum of Garden History at Lambeth (next to Lambeth Palace and Lambeth Bridge). Ernest Shackleton has a blue plaque is on Aberdeen House (now St Davids) at Westwood Hill near Crystal Palace. Joseph Banks used to live at 32 Soho Square, in the building now occupied by 20th Century Fox. There is an engraved memorial on the wall. Thomas Henry Huxley, who went on an epic voyage on board the Rattlesnake in the 1840s has a plaque at St Johns Wood (near Abbey Road).
Graves: Not many graves exist in Greater London. As exploration was a dangerous activity, many perished at sea. Others have become simply lost. For example, William Dampier, Samuel Wallis and Matthew Flinders were buried in England but their graves have been lost. Drake, Cook, Franklin, Bass, and Scott died while on voyages. Shackleton is buried in South Georgia. Charles Clerke from Cook's third voyage is buried on the Kamchatka Peninsula.
The graves that can be visited in the London area are: John Ross, Robert McCormick, Robert Brown, and Archibald Menzies, and John Stuart are all at Kensal Green Cemetery. Captain Robert Fitzroy is at All Saints Church in Upper Norwood. William Bligh's tomb is at the Gardening Museum next to Lambeth Palace. Joseph Banks' grave is at St Leonard's Church in Heston (west of London) but the exact location is lost. James Clark Ross is at The Abbey, Aston Abbotts in Buckinghamshire. Edmund Halley is at St Margaret's Churchyard in Lewisham behind Greenwich (same grave as Pond) and not marked.
John Harrison, inventor of the marine chronometer is at St John's Church, Hampstead, as is William Westall, landscape artist on Flinders' Investigator voyage. There is a plaque to Thomas Harriot in the Bank of England (viewable by appointment) as he was buried where the bank now stands. Joseph Hooker is buried at St Anne's Church, Kew.
Other: There is a replica Golden Hinde on Southbank near London Bridge. Dulwich College has the James Caird that Shackleton made his epic 1916 rescue journey with. More of John Harrison's clocks and marine chronometers are at the Clockmakers' Museum next to the Guildhall and in British Museum (Room 38 & 39). There are also busts to Joseph Banks in the British Museum's Enlightenment Gallery and the Chelsea Physic Garden. The Royal Geographical Society in Kensington sometimes hosts talks about the history of exploration, as does the Zoological Society of London. The Royal Botanical Gardens at Kew sometimes have exhibitions related to the great voyages of exploration that brought have botanical specimens. The herbarium in the Botany Library at the Natural History Museum (Kensington) also have most of the botanical specimens brought back on Cook's voyages and they can be viewed by appointment.