There are a number of organisations who may be responsible, depending on whether the drain is inside property boundaries or, part of a public network. The initial points of contact for any blockages would be the water company or the highways authority.
If there is flooding in the road, you should contact the highways department of your local authority who will take appropriate action to resolve the situation. The Citizens Advice provide more information on this; for a link to their website and, to find your local council please see the websites in Related Information.