from the actual terms and conditions:
we will not cover your vehicle if it is
• used on a regular basis for shopping, commuting to and from work, or to transport friends and family
• driven more than 8,000km during a 12 month period, or
• used for a business purpose or for hire,
The key word there is used on a regular basis
that's probably why they won't insure you. As you would have to use it to do shopping on a regular basis?
To say they won't cover you if you are heading to the shops at all is odd. I would say it has more to do with the fact you don't have another car.