Looking back through my inbox, I've found some confirmation emails from Easyjet for flights I have booked in the past.

The last flight I booked was back in in January though, so maybe they have changed their email policy since then.

I think as long as you have the 6 digit booking reference then you should be ok as I don't think Easyjet will issue a booking without having cleared payment.

It is worth checking when you are viewing your booking if they have a facility to re-email you a confirmation, and that the email address registered is correct.