What radiator for very cold basement in house?

 Bit confusing this. You might be stricken with condensation on those cold concrete walls so the plumbers advice for moving the warm air around is a good one but of course you will use more gas Warm moist air from the cooking wont help so an extractor to the outside over the cooker would be a good thing. Good luck!

Your problem may be due to damp if it's in the basement, as many old properties lack good damp proofing. Try installing a de-humidifier, to dry the area out and if I was you I would opt for a small wood burner (vented to the outside) to suplement your radiator in cold weather, as the heat from the fire willl assist drying out the walls etc....

There are standard calculations that allow one to work out the correct size [or heat output] of radiator given the cubic size of the room and taking into factors such as is the room particularly liable to be cold, likely weather conditions etc.   A plumber who is familiar with heating systems should know their stuff regarding this.We asked our plumber to upgrade the radiator in one of our rooms because the one already there just wasn;t doing the job.  We suggested one X amount bigger, he installed one more that twice as big as that insisting that was correct.  We suspiciously  thought maybe he was having us on and just wanted to shift this giant radiator he may have had in stock.  However, the proof of the pudding was that the radiator he fitted was perfect and the room is just right in the winter now.If you think your plumber knows his stuff, take his advice......   

To find out what radiator size you need for a room try the below link http://www.radcalcs.com/ and work out the BTU for each room. I suspect that if you get one of the fan radiators that are so common in Italy, you may be able to get away with a smaller BTU rating. If your room is damp, as well as cold, however, you will need to think about a dehumidifier as Gromit says or you may just be moving a condensation problem around the house. The fan radiators are very effective for heat output but I would consider the idea of a small vented woodburner if you can.

My place has an ][old] fan assisted radiator - its brilliant.  Normally i don't use the fan part [so it works like a normal radiator], but in Winter, when i first get to the house I switch on the fan - the rise in temperature is noticeable and pretty quick, In my lounge [approx 5m by 10m with concrete floors and ceiling and no double glazing], we get a 2 degree rise within 30 minutes or soif you take the cover off mine it looks like a big car radiator [lots of fins for heat exchange] - but you do need to ensure that it gets a good supply of hot water from the Central Heating system