Not unless I was getting reimbursed for motoring costs
If your employer orders you to transport colleagues as part of your job, you are getting very close to needing "hire or reward" insurance. You would be in a very, very interesting position if the question were raised as to whether you were driving "on the clock" as a driver, rather than as an incidental part of your job. It's one thing to make a journey as part of your job (which alone requires Class 1 business use), and if you have passengers, so be it.
But to make a journey that you would not yourself make for the purpose of moving someone else, in your own car? Most large employers who need staff to do that will have pool cars, or get rentals, precisely to avoid the uncertainty about insurance.
The first test would be "can I refuse to make this journey and not invoke disciplinary action?" If the answer is "no", then you're driving as part of your employment.
The second test would be "is this journey an incidental part of my job, such as going from one customer to another or one site at which I work to another, or is the journey for the sole purpose of moving something or someone else?" If it's a journey you wouldn't otherwise make (ie, you're just the driver, not the cargo), then that's as a minimum Class 3 business use. Even then I would want to write to my insurer and tell them exactly what I was doing and get them to write to me explicitly saying I am covered.