They can't access your bank account. Even if you sent them a cheque which shows your name, bank account number and signature they still couldn't.
But this is a scam. You haven't even entered a lottery so you much realise that.
Can you please open the headers to the email to see where it originated from - if you don't know how to do that there are good instructions here:
http://www.emailaddressmanager.com/tips/header .html
Everyone who uses email should be familiar with headers.
You are probably going to be bombarded with cold callers trying to flog you stuff you don't want, or even worse get phone calls pretending to be officials who need your very personal details. Be alert when you answer the phone.
If any official from the bank, council or anywhere telephones you, take their name and call the company back to check it is legitimate before discussing anything.