A conservatory is considered to be a permitted development, not needing planning permission subject to certain conditions. You can find the full planning permission terms at the planning portal. You can also find informaiton for the New Forest and the Hampshire County Council.
The website explains the overall size of the conservatory, what elevation or side of the building it's permitted to be on, height and all other factors to consider. Our expert team can advise on this if you are in any doubt.