blankets

So its 145am my girl keeps waking up screaming. its really cold tonight and i dont know if shes cold too she has a long sleeve thick grow on and a 2.5 tog sleeping bag (im in the UK) ive wrapped a blanket around her while im feeding her question is is it safe to put her into the cot with this blanket wrapped around her shes very strong can walk crawl stand roll im just worried but its so cold and our heating is only controlled by going up and downstairs. does anyones baby sleep with blankets?