My possible solution would be to start earlier, drive your personal vehicle to the depot at 6 or 7 in the morning and take off in the company vehicle, then you could start your time when you leave your depot (6:30-7ish) and then you would be able to avoid traffic. That way you wouldnt feel that you are "working for nothing", breaking UK employment laws, having to report company vehicle use for personal use, etc. You also would not have to have the company vehicle in your drive taking up your space (I do not know UK tax laws, but personal storage of a company asset may be something you need to report).

I believe under this scenario, all potential problems are solved. Please inform me if they are not, and if you bring up the issue with your employer about the "working for nothing/breaking of UK employment law" I am sure that they would be willing to agree to this arrangement to ensure full compliance.