I know, in some area, some houses are required to have the rooftop run-off water be led away to the public sewage through a "well structure" as you described. If that is the case, your house will have no sump pump system and when the "well" is plugged, water cannot run away from the house and will stay around the foundations, then there is a great chance it will sip into the basement when the water table get higher and higher. The consequences may be disastrous if the problem left unattended. You should call the professionals in to look at it right away.
What your situation now is the "well" is plugged and water runs on the lawn already, I guess. Make sure the water runs all the way over to the public sewage drains, I suspect the grading of your lot may create an undesired water channel to your neighbor (most likely the one at your back) and that is why a "well" structure is required for your house in this case.