Re-reviewing this, as I found the power sockets! They're in the 'snug', appropriately - as you walk in, go far left. They're under the bench seating. There are like 4 power sockets, I think.
Free Wi-Fi. No password. Boom. You're online! Leon is popular with laptop-toters in Spitalfields Market - and with comfy benches, no-fuss free Internet access and friendly staff, it's easy to see why. Could do with more power outlets, but that's always the way, right? And it's a bit loud. But for checking your email and quick tasks, it's perfect.