Yes, and with less paperwork than the town's age would suggest. Flitwick has a handful of listed buildings. It has no conservation areas at all. The neighbours are extending at a steady clip. The thing most likely to slow a project down is the clay underneath, which cares about foundations more than any planning officer does.
Flitwick has 15 listed buildings: 1 at Grade I, 1 at Grade II* and 13 at Grade II. Listing covers the whole building, inside and out, so on any of those 15 even a new window or an internal wall needs listed building consent from the council on top of any planning permission. For a place that turns up in the Domesday Book in 1086, nine centuries have left a remarkably short list of things you are not allowed to touch. If your house is not one of the 15, listing does not come into it.
There is 1 scheduled monument in the area, The Mount, the Norman motte and bailey castle. Scheduling is the strictest protection there is, and it matters to the handful of owners whose gardens back onto the earthworks rather than to anyone planning a kitchen on an estate.
Plenty of people are getting on with it. Central Bedfordshire's planning register shows 1,196 applications in Flitwick between April 2024 and June 2026, with 532 of them in the last twelve months. That is a town with skips on the drive and scaffolding going up somewhere most weeks, and a reasonable sign that the semi you are viewing has a neighbour who has already tested the rules.
The ground is the part that needs a professional opinion. The British Geological Survey rates Flitwick at class 3 on its shrink-swell hazard scale, and the whole area reaches that class. Shrink-swell means clay soil that swells when wet and shrinks when dry, and on clay like this an extension usually needs deeper foundations than it would on firmer ground, particularly near large trees. Get a structural engineer to look at the soil and any trees close to where the extension would go while you are still costing the build, since foundation depth can move the budget more than the choice of kitchen.
In practice, most Flitwick houses keep their full permitted development rights, because there are no conservation areas to take them away and only 15 buildings are listed. Many single-storey rear extensions and loft conversions can go ahead within the national size limits without a full planning application, while anything larger, anything on a listed building and anything on a flat goes through the council. Building regulations apply either way, and on this clay the building inspector will have views on the foundations.
Freedom to extend is one of Flitwick's real strengths, with planning rules that rarely get in the way and clay that asks for a proper set of foundations.