Yes, it is possible. All the merchant actually needs to get an authorisation code is the card number, expiry date, and the amount to be charged. An authorisation code only guarantees that the card has available funds, and hasn't been reported lost or stolen.
Given the high risk of fraud, it's unusual for a merchant not to also ask for the CV2 and the address details. By asking for these details, merchants can make use of fraud checking services offered by banks and merchant account providers.
If a merchant does choose to ask for address details, they're usually making use of a service called the Address Verification Service (AVS). It only checks the postcode and the numerals in the address though. If you lived in 10 Downing Street, for example, the AVS would check only the following information: 10, SW1A 2AA
It might not have been terribly difficult for fraudsters to find your home number and postcode, and thus pass an AVS check, but it is also possible that they've found a merchant with lax acceptance criteria. For example, the merchant might ask for a shipping address, but not actually run any security checks on it.