Yes, and your neighbours already have. Heritage rules barely apply here. Almost every house is too new to be listed. Planning applications arrive at a steady rate. The main thing standing between you and a bigger kitchen is the clay underneath it.
Winnersh has 9 listed buildings, and all 9 are Grade II. None is Grade I or Grade II*. Listing means any change to a building's character, inside or out, needs listed building consent on top of any planning permission, and that can cover windows, doors and internal walls as well as extensions. With 9 in a place this size, the chance that your house is one of them is small. Check anyway. Nobody wants to find out after the builders have started.
One conservation area falls within the Winnersh area. Inside a conservation area, some changes that would otherwise go ahead without an application can need consent, and the council can add further restrictions on top. It's a single area in an otherwise unrestricted place, so the address decides whether it touches you.
The planning register for the area shows 841 applications between April 2024 and June 2026, with 386 of them in the twelve months to June 2026. That's a lot of loft conversions, rear extensions and garage conversions for a village of mostly post-war and later houses. Winnersh wasn't built with a spare bedroom for everyone who wanted one, and residents are adding them one application at a time.
The ground is the real constraint. The British Geological Survey puts Winnersh's shrink-swell hazard at class 3, and all of the area reaches that class. Clay soils like this swell when wet and shrink when dry, which moves foundations over the years. For an extension, that means deeper foundations than a builder might first quote, attention to nearby trees, and a structural engineer's view before anyone starts digging. It's manageable. It will cost more, and the extension should be budgeted for that, not surprised by it.
In practice, most Winnersh homes aren't listed and aren't in the conservation area. Many modest extensions can then go ahead under permitted development, without a full planning application, as long as they meet the national size and design limits. Anything bigger, or anything on a listed building or in the conservation area, needs the council's consent. Confirm which applies to your address with the council before paying an architect to draw something ambitious.
Your freedom to extend in Winnersh is one of its real strengths: few heritage restrictions and plenty of neighbours who've done it already. Just budget for deeper foundations.