You've worked out petrol and parking costs, but not the rest of the cost of running a car. However, you'd have to pay these costs anyway and some of these are fixed whether or not you use your car (tax, depreciation, insurance, MOT, breakdown cover), only tyres and other maintenance increases the more you use your car.
Or course, if you're using your car for work, you can reasonably expect your employer to pay the standard 45 pence per mile to cover the whole cost of running a car, not just petrol.
Another simpler way of working out fuel costs would be to use the HMRC fuel only rates, which does all the fiddly maths for you. However, in my experience, these aren't very generous and only fully cover the cost of fuel if you're on a good run at 50-60 MPH. Any stop start traffic, or motorway speed, and they underpay by about 10-20%
www.gov.uk/guidance/advisory-fuel-rates
But in most cases, once you have a car, you might as well use it, because the marginal cost of doing so is almost certainly cheaper than public transport and also in most cases quicker and more convenient - you don't have to wait for the train to come, you mention carrying heavy things.
Generally, the only time the train is a cheaper or quicker option for a car owner is when parking is difficult and/or expensive, you have to pay a congestion charge, you're driving to a very congested area or you'd rather be able to drink alcohol than have access to your car.