Assuming the house was built to the regulations in force in the UK in 2010 then the insulation level in the walls is adequate for UK conditions - a shockingly late development compared to elsewhere in Northern Europe.
Thus there can only be one underlying reason for the condensation: inadequate heating. An occupied dwelling is constantly subject to atmospheric humidity which comes about by washing, bathing/showering, drying anything including wet outdoor clothing hanging on a hook, wet footwear, etc., etc. No less significant than those mentioned is the breath of the occupants, including any animals - even plants and their pots emit humidity as does food. None of this is the fault of the building.
As with most people, you may be familiar with how fridges either frost up or otherwise collect condensation that drips down to the motor (and it evaporates from there due to the heat the motor generates - the moisture comes from the stored food. What happens in an unheated house is exactly the same phenomenon - cold walls (especially if covered with curtains) cause the air at them to reach dew point, shedding its humidity in the form of condensation. When walls are constantly wet then the consequences will inevitably be just what you describe. The effect will be particularly pronounced if the common habit of keeping all internal doors closed is practised - common where heating is near non-existent or absent altogether. The condensation risk is always far worse in older buildings due to the absence of insulation - the walls remain reluctant to warm up. As with a glass bottle straight out of the fridge, a cold wall will produce condensation whether it is external or internal. A wall or any object at a temperature of 15 degrees or higher (internal or external) will not generally gather any condensation in the UK - a modest target for a dwelling.
Yes, if you ran enough dehumidifier (a kind of refrigerating machine) capacity in the house then you would dry the air sufficiently to avoid dew point being reached at the walls. But you would have to pay the not insignificant cost of the electricity used.
There is the other option of venting sufficiently to the outdoors to have a rapid rate of air change - replacement of the air in the house by air from outside. There is no guarantee that the vents seen on windows in the UK (I have not seen them elsewhere) on windows will be sufficient, in fact I doubt it very much if the dwelling is effectively unheated. If you choose venting then you are to a degree living outdoors, something not many would choose.
I have a property which has been let for years. The last tenants left on good terms but complained about dampness. As is so common in the UK, they only turned the heating on for an hour or two twice a day, no matter what/how I advised and explained. This level of heating makes very little difference in the scheme of things and additionally is extremely inefficient and proportionately very expensive - just like switching on a car engine and running it at full throttle for a few miles, then switching off the engine to coast to a halt and starting all over again. Think how inefficient it is to make long journey (the UK winter) this way. Everyone knows the most efficient way is a steady speed. To make matters worse, those tenants covered all the radiators with wet washing. No wonder that the place became sodden to the point where the paint on the outside of the outer doors was covered in water blisters. The moisture was actually coming out through the wood, and they were in the process of ruining the place. But there are legions like them (in the UK) and the subject of dampness regularly comes up here on AB. I have made these comments several times in my postings in response. An awful lot of people, including those who are "experts" simply don't seem to understand the basic physics of this issue. This is surprising given that the UK's atmosphere is and has been particularly damp to start with.