Energy suppliers have a cooling-off period of 14 days, which starts from the date you submit your switch, so no action is taken until this period is over. The switch process can take up to four to six weeks to complete, depending on supplier, although some will now switch you more quickly.
But don't worry, you won't lose your supply during this time. It should be a seamless handover from one provider to the other. All that's really changing is the billing, not the actual gas and electricity that you're supplied.
Energy suppliers are supposed to keep you updated on your switch (via letter/telephone/email - please keep an eye on your junk/spam folder). If you ever have any queries about your switch, you can always contact your energy supplier for an update.