Unfortunately, if you've lost access to your email account it appears instagram are not going to help you retrieve your account.

If you've forgotten your password and lost access to your email account, we're unable to release the Instagram account to you. This includes accounts registered with mistyped email addresses.
We understand this can be frustrating, but this policy is meant to make sure Instagram accounts don't fall into the wrong hands. We hope that you're able to remember your password so you can log in and correct your email address.

Instagram Help Center: I've lost access to the email I used when I signed up.

Your best bet is try to regain access to the email address you used to create your original account.