Yes.
You can switch without exit fees up to 49 days before your tariff ends. If you can save money, it makes sense to do the switch sooner rather than later. But if you'll be moving to a more expensive tariff, it's better to stay where you are until the last moment.
You can usually pick the date of your switch with the new provider, and with the 'faster switching' initiative, it can be as quick as five working days from when you apply. Though it's worth noting that even if you select a day, there's no guarantee it'll happen then (though the supplier will aim for that date).
Most providers will give you up to 21 working days to complete the switch - if the option isn't available on their website, contact the new supplier to see if it can offer this.
If you do a switch through Cheap Energy Club, you can choose to switch immediately (taking up to five working days), or you can choose to switch after your 14-day cooling-off period.