We have a small fan heater for a room that doesn't have a radiator and I will tell you that it costs outrageous amounts of money like 30p/hour. I also wouldn't consider them safe in a child's room, honestly, especially to leave on all night. Another alternative to the ones Kirsty has suggested is to turn all but baby's radiator off at night so you're only paying for the one but that will still be costly. We have ours set to turn on if her bedroom drops below 17.5, and she's warm enough in a long-sleeved vest, long-sleeved pyjamas and a 4tog duvet. She also has a little heat-up teddy she takes to bed that gets her nice and warm at the start of the night which helps.
Just wrap her up well, my little one is 18 months and we've just added a thick duvet and pillow on her bed.
We use 2.5-3 tog sleeping bags and layers. We keep the heating on during the evening and then I’ve been turning the thermostat quite low & the temp gauge so that it turns off for most/all of the night but if it drops below a certain temperature then it will come back on. Have you got a room thermometer to gauge? That can help for dressing. My girl likes to be warm so would generally only be affected if below 18 degrees. Of course they guide 16-20 is optimal but I think 16/17 feels freezing.
Can you not get warmer pj's??? Putting the heating on timed and just take the edge off over night? I wouldn't leave a heater going all night in her room xx