It's vital that you check policy wording before committing yourself.
We checked the policy of our usual travel insurer and discovered that although hiking was covered (along with canyoning, water-skiing, canoeing and much more), hiking about 2000 meters was specifically excluded. This was a great shame as our insurer is one of the lowest cost travel insurers in the market.
After some research we eventually insured with an alternative insurer - which at £29.97 for two people for 20 days was a bearable expense.