You must realise that insuring a laptop for a responsible adult is a completely different proposition to insuring it for a teenager's first trip away from home. Because some people will happily leave a bag that obviously contains a laptop lying around in a busy place while they are concentrating on other things, some companies are reluctant to insure laptops.
I hope that you find a policy with some sort of cover but your main protection should come from your own precautions.
There are devices that come in 2 parts. One part is a chunky sticker that goes on the laptop. The other part is like a key ring fob. If the two parts are ever more than a couple of metres apart, the alarm sounds. Physical cable locks are also available.
You should also put passwords onto the computer so that anyone who takes it cannot read your data or log on to any sites that you use.
You should also investigate whether there will be safe places to leave valuables if you will be going out without the laptop while away.
You should also keep a note of the serial number and engrave your name and postcode onto the laptop.
Googling for "laptop security" will get you more advice. Of course, if you can manage without the laptop, that could be the safest option.