Removing atmospheric moisture from a house

We tend not to use our heating that much.
We do have dehumidifiers but they are relatively expensive to run

That's your problem. Dehumidifiers work better in warm rooms as warm air holds significantly more moisture than cold air. You are doing the equivalent of pushing water uphill. Expensive and useless.

Neither. Dehumidifier. It really does work very effectively (and cheaply) if you've bought the right one and use it when the air is warm. When my house is cold and damp I'm lucky to pull out 2L, but once the house has been warmed up a few degrees it can pull out 12L. A significant difference, and it also helps to heat the room up. Check you've got the right one.

New build houses are now all being fitted with MVHR (mechanical ventilation and heat recovery) systems. They can be retro fitted but there’s a lot of ductwork. In your case I would have thought extraction fans better…

Google seems to agree (I was curious myself!):
Using an extractor fan is generally better and more energy-efficient than opening wide windows when your house is warm and the heating has been on.

Why an Extractor Fan is Better
Targeted moisture removal: Extractor fans pull out humid air directly from the specific source (like the bathroom or kitchen) before it spreads to cooler rooms.
Heat retention: Running a fan removes moist air without flushing out all the stored heat in your walls, furniture, and indoor air.
Avoiding drafts: Opening windows lets out large amounts of expensive, warmed air quickly, forcing your heating system to work harder to warm the house back up.

When to Open Windows Instead
Short, sharp air-changes ("burping the house"): If you need to air out a room thoroughly, opening windows wide on opposite sides of the house for just 5 to 10 minutes creates a fast cross-draft that swaps the air out before the building's thermal mass cools down too much.
High moisture/after a long shower or cooking: If an extractor fan isn't powerful enough on its own, a quick window crack combined with the fan can help speed things up.
Mild weather: If the outdoor air isn't freezing cold, a brief window opening is fine, though you should turn down the radiator in that room first so you aren't heating the outside

If our cooking is generating steam, we shut the kitchen door and open the window a little, and only close the window when serving the food. in an open plan area this wouldn't work so I think an extractor fan over the cooker would be your best bet.

Isn't that partly because warm air holds more water than cold air? Opening doors and windows work because you are exchanging hot damp air with colder less damp air.

Instead of condensing dehumidifier look at a desiccant one.

Windows. Always

what age is your property?

Windows will be best for the property and your health.

Do you have solar panels? We don't line dry in the winter but have dehumdifiers in the spare room with the clothes horse things. But we have solar panels, and on a sunny day this means we've used no electricity, and we have a solar panel battery for storing excess energy. Do you have an extractor hood over the hob? This works well fo rus in the kitchen.

When you are cooking, have the kitchen window open and the door shut.

Keep your bathroom door closed at all times, and open the window for at least half an hour after a bath or shower.

It does make a big difference. Most people don't understand that if you keep the humidity low you can run the house 2-3C lower in temperature and it feels the same. Heating it just continues to suspend moisture in the air.

I suspect this is why a lot of people complain that they can only tolerate 20C when others find 15C fine.

Some tricks I don't think have been mentioned :

Kitchens : Keep the extractors on when you are cooking, and keep lids on boiling pans. The water vapour condenses on the lid and rolls back down into the pans rather than into the atmosphere increasing the humidity. You can also use steamers for vegetables etc.

Bathrooms : After you have showered use one of those rubber squeegees to push all the water off the screens and in the bath down the plughole. This is all water that will evapourate contributing to the house humidity. It has the added advantage that you will keep the screens cleaner as when you remove the water far fewer mineral deposits precipitate out onto the glass screens.

Windows : Windows are great free dehumidifiers. Use a window vac or just a cloth to remove the water.

Clothes : Drying clothes on radiators produces humidity. If you must do it do it in a small room that is closed off with a dehumidifier in there.

Monitors : You can get little temperature and humidity monitors to place in each room to monitor the humidity.

Extractors are best where there is concentrated humidity in the air, like bathrooms and kitchens. Running electric fans is relatively cheap in electric terms, but fans do wear out so eventually there is a replacement cost which is often a lot more expensive than the electricity running the fan.

Oh and dehumidifiers vary in efficiency, especially at lower temperatures.

The more common types (condenser) are better I think over 15C. If you are running a lot less than that then dessicant is much more efficient.

Extractor fans use very little electricity, you should definitely use them while you're cooking or showering.

I squeegee the shower and then open the bathroom window for 5 minutes after showering and find that this drops the humidity from 85%ish to 65%ish. The air temperature drops about 0.5C in this time but rebounds very quickly because it's mainly warm, moist air that has been lost and the fabric of the room stays warm. The extractor fan then deals with the remaining moisture in the air within a few minutes.

Keep the windows shut use a dehumidifier. When you open a window cold damp air comes in that’s physics! Matter or mass cannot be created or destroyed!