Colin Prescot, 53, and Andy Elson, 48, hope to set a new world record by flying their 387-metre craft - the QinetiQ 1 - to 39,600 metres.
The intrepid pair set off in a boat from St Ives beach in Cornwall for a larger ship, from which they hope to launch an helium balloon the size of a football stadium.
But owing to unfavourable cloud conditions, they must now wait until Wednesday before attempting lift-off from the spot in south-west England, a spokesman said late on Monday.
"Conditions were not suitable for the launch (on Tuesday). All being well, it will happen as planned on Wednesday morning," he said.
The pilots plan to drift to the edge of space for an hour and conduct experiments on the stratosphere before returning to earth and, they hope, a place in the history books.