One of the issues with parking near White Hart Lane is that much of the area is under controlled zone parking. This means that if you park in certain areas you will face the legal consequences. For some people this will mean a fine whereas for others and this could mean actually having your car towed away. If your car does get turned away you will be expected to pay for it releasing and this can run into the hundreds of pounds.
People who want to attend matches and who want to park legally and safe will always make sure they know where the controlled zones are. You can find this out by looking online or simply taking note of what street signs in the local areas advise you of. So if you want to avoid having to pay more money than usual for parking never park in a restricted zone.