problem starting engine when cold?

I have problem on my r reg Ka, keeping the engine running on first start of day, plenty of power, engine turns over immediately but have to catch revs and keep pressing accelerater or it will cut out whilst still stationary. Once it gets going it appears to idle fine though sometimes cuts out in traffic jams but restarts fine rest of the day. In addition, sometimes sense an over rev on changing gear. Any help would be greatfully appreciated