British Airways allows US Exec Club members to upgrade from full fare economy/Club to the next class of service - no double upgrades allowed. I don't think that UK or Global members can do this. Since BA doesn't hand out upgrade certificates, this is the only way to be sure of an upgrade... all other upgrades are at the discretion of the BA employees one encounters.
somewhat OMNI: BA has a "necessity only" policy for upgrades from Club to First, but my sister tells me that she has struck gold the last two times she flew with them, and may find it hard to go back to life in Club