Yes, and the heritage rules will barely notice. Only a handful of buildings are listed. No conservation area covers the place. The neighbours send in planning applications all the time. The biggest obstacle to your extension is your budget.
Historic England's list holds 7 listed buildings in the area: one at Grade I, none at Grade II*, and six at Grade II. Listing covers the whole building, inside and out, so almost any change to one of those seven needs listed building consent, and replacing windows or knocking through a wall becomes a formal process rather than a weekend job. Seven out of a place this size means the odds are strongly against your house being one of them, but check the listing entry before assuming. No conservation area and no scheduled monument were counted within the area either, so nobody from the heritage side will be asking about your window frames.
The neighbours treat this as licence, and they're right to. West Berkshire's planning register logged 2,037 applications across the area between February 2024 and June 2026, 905 of them in the most recent twelve months. That's the sound of a place adding rear extensions, loft rooms and garage conversions to post-war and later houses, which were never listed and mostly never will be. A street where half the houses have already grown a kitchen extension makes a poor case for refusing yours.
In practice, many modest single-storey rear extensions, loft conversions and outbuildings on an ordinary house can go ahead under permitted development rights, without a full planning application, as long as they stay within the national size and design limits. Bigger or more visible schemes need planning permission in the usual way. Two checks matter more here than heritage: whether permitted development rights were removed when the estate was built, which the council can confirm, and whether the title deeds carry restrictive covenants from the developer. A plain-looking cul-de-sac can hide a 1980s clause about porches. Ask for a lawful development certificate if there's any doubt, because "the neighbour did it" won't persuade a planning officer.
For anyone who wants to add space, Burghfield Common is one of the easier places around: no conservation area, only a few listed buildings, and a planning register full of neighbours doing the same. Where there's a hurdle, it's more likely to be in the deeds than in the heritage rules.