Yes, and heritage rules are unlikely to be what stops you. There are two listed buildings in the whole area. There are no conservation areas. The neighbours have filed hundreds of planning applications in two years. The likelier obstacle is the neighbour, not the heritage rules.
The National Heritage List records two listed buildings in the area, and both are grade II. There are none at grade I or grade II*. Listing means changes to the building itself, inside or out, need listed building consent on top of any planning permission, and that process is slower and pickier. With two in the whole area, the odds that the house you're viewing is one of them are slim, but check the listing before you plan the kitchen. There are also no conservation areas inside the area. The conservation areas that appear nearby, Telscombe Village among them, sit outside it, so the extra controls on alterations that come with a conservation area don't apply to these streets.
Two scheduled monuments sit within the area. That is the strictest tier of protection in England, and it mostly matters for land close to one, out on the downland of Telscombe Tye, not for a semi wanting a rear extension.
The neighbours clearly aren't shy. The planning records show 463 applications between April 2024 and June 2026, 189 of them in the last twelve months. That volume describes people actively trying to change their homes. It says nothing about how many were approved, and no one should read an approval rate into it. It does tell you that a buyer planning an extension is joining a queue rather than starting a trend.
In practice, many single-storey rear extensions and loft conversions on houses may fall under permitted development, the national rules that allow some work without a full planning application. Anything bigger, anything facing the street, and most changes to flats will need consent from the district council. Ask the council for a lawful development certificate before building work starts, so a future buyer's solicitor has nothing to argue about. Also look for any conditions attached to the original estate that remove permitted development rights, because the paperwork on the house can override the national rules.
Freedom to extend is one of Telscombe Cliffs' stronger points, with almost nothing on the heritage side standing in the way. What holds a project back here is more likely to be the budget or the neighbour than the building's history.