Depends on the small print of your motor insurance policy. It used to be the case that travel to and from a fixed work location was covered, but any work travel outside that (e.g. visiting a customer or a different site) wasn't - you needed to buy "business use" as an add-on. I got bit by that in the 90's when I had an accident as I didn't know the cover was needed (fortunately they accepted it was a rare occurrence after my employer intervened). Things like sales jobs where lots of mileage would be involved needed another level of coverage again.
What I noticed last time I shopped around was that travel to and from work wasn't covered by some providers, or worded so ambiguously you couldn't be sure, so you ended up paying a bit more to make sure.