Mostly yes, but the answer depends a lot on which street you bought on. There are 38 listed buildings in the area. Two conservation areas cover the most architecturally sensitive corners. There are no scheduled monuments inside the boundary. Anyone outside the conservation areas and not in a listed property has roughly the same freedoms a standard suburban postcode offers; anyone inside is in for a longer conversation with the council.
The listed stock is small but real. One building holds Grade Two-star status. The other 37 are Grade Two. None reach Grade One. Listing means a separate consent on top of any planning permission for almost any change that touches the character of the building, which includes windows, doors, internal walls, materials, and often colour. The headline rule is that the work cannot harm the special interest of the property, which in practice means a planning officer is going to want photographs, drawings, and a heritage statement explaining why the change deserves to happen. People who buy a listed house and then discover what they have signed up for typically discover it during the second quotation rather than the first.
The two conservation areas are named for Daedalus, the former naval air station, and for Lee-on-the-Solent itself. A conservation area does not freeze a property in place. It does change which works count as permitted development and which need explicit consent. Demolition, alterations to chimneys and roofs, certain extensions, satellite dishes, and the removal of trees over a defined trunk size can all need separate paperwork inside one. Roof tiles, front doors, windows, chimneys, and the kerbside arrangements of wheelie bins all come into a conservation officer's view, and most homeowners discover this when they discover it.
Outside the conservation areas, and assuming the property is not listed, the standard permitted-development rules cover most extensions and modest alterations that would otherwise pass without comment. A loft conversion, a single-storey rear extension, a porch within the normal volume thresholds, a side wraparound where the plot allows it: these are routine, and large numbers of them happen in the area every year. Across the last twelve months there were about 413 planning applications recorded in the wider postcode set. That is the work-rate of a place that is renovating, extending, and tidying itself up rather than rebuilding wholesale.
The practical version of the answer is to check the listing register and the conservation-area boundary before falling in love with the brick. The rules are not unusually onerous, but they exist where they exist, and the boundary lines are not where you might guess them to be.
Medium freedom to alter and extend, more constrained at the seafront character end and almost unconstrained at the post-war semi end. The honest answer is the property line on the planning portal, not the postcode.