Depends on your insurer - no extra cost on mine.
Cars are usually insured for Social, Domestic and Pleasure - driving to work can (and usually is) classed as business.
Occasionally the penny pinchers will check a travel claim and if you aren't insured for Business they can stop any payment.
I've been out a few years now and the company i work for like you to have it as well, covers their arse as well as yours if you have to go somewhere on company business and use your own car.
It's only classed as a business journey if you receive some remuneration for using your vehicle to travel to or from your normal place of work.
you can opt for SDP+commuting which covers your journey to and from your normal place of business but you dont get fuel money or another form of allowance towards running the vehicle.
of course if you then use your car during the course of your duties for work related purposes (is driving to a meeting off site, transporting documents etc) then you need business class insurance.
You are best being honest with your insurers, if you tell them it's registered at your home address but realistically it spends only 10 days of of the 10 weeks you are Halton at your home address you will have broken the T&C's, as you need to tell them where the vehicle will be spending most of its time.
i have seen (at the roadside) insurance companies cancel someone's cover as they lied about where the vehicle was being kept for over half of the week. No insurance means people like me come along and whack 6 points on your licence and make your wallet £300 lighter.
For what it's worth my insurers when I went through the College of Knowledge just simply placed a note on my file stating the vehicle would be in Sleaford for 32 weeks, no additional charges.
the final thing is that I'm sure to take a vehicle onto camp,and keep it their it needs to be taxed, MOT'd and insured.