I have had itchy palms for a few months now. I came across this forum through Google whilst trying to find the cause and a cure and as I've found something which worked for me I thought I'd let people know. A couple of weeks ago I tried the homeopathic remedy called Lycopodium. First of all I took Lycopodium 6 which relieved the itch for up to an hour - often taking up to 6 a day and I have just taken Lyc 200 - one night and morning for 5 days and the itch has almost gone. If you are interested in trying this you can google for sites which sell the remedy (you may be able to buy Lyc 6 in chemists) and also for guidance on how to take homeopathich remedies (you should avoid coffee and mint and not eat for 10 mins either side of taking the tablet.
I hope someone finds this helpful.