KE Adventure (01768 773966; keadventure.com) has run its lodge-based Everest Base Camp Trek for 30 years; 17 days from £2,195 including all meals and flights. Departures October to May.
South America Overland
Dragoman runs some of the best overland expedition trucks in the business with views from roof seats on slow dirt roads and a maximum of 22 on board. Ask sales staff for the sex and age of those currently booked to make sure you’re a fit. Two-week tasters take in a couple of countries but a run from La Paz down the spine of the Andes into Patagonia is the big adventure.