We've been looking at insuring our kart and trailer for both storage at home and while at/travelling to races.
So far I've found Ryan Motorsport Insurance (
www.ryanmi.com/en) and Moris Motorsport Insurance (
www.moris.co.uk) who offer this sort of insurance. From the quotes we've had from both, they cover the kart, engine and around £1,000 of spares for about £220 per year (can't pay monthly). The only thing with Moris is that you need to have a tracker fitted to the kart/trailer which is an additional £60 and you can't have a policy with them unless you purchase the tracker as well.
You can request a quote from both on their websites and they came back to us with a price in about 48 hours.
Hope this helps!