In the UK, companies very rarely offer you a company car unless they expect you to be doing a lot of travelling for the company. This is because in the UK company cars are taxed quite heavily, unless you are actually going to be using the company car for lots of travelling on company business.
If your job is going to involve significant travelling for business, then it may be hard to turn down the car. Companies usually offer them because it is cheaper for them to give you a car to use, and pay the costs of your using it, than it is for them to reimburse you for using your own car. If you are representing the company they may also not want you to use your own car while on company business, if it is older or quirky. They may not allow you the choice. But then you also don't want to turn the car down. It will be a low-tax perk, and any extra money you get is unlikely to be enough to pay for running your own car (remembering that you will have to pay tax also on any salary you get instead of the car).
If you are not going to be travelling for company business, then the company doesn't care about the car, they just think of it as a perk. It should be easy to turn down the car, and get some money in return. It may not be as much as you would like, because companies can get cars very cheap if they are managing a fleet of them.
By the way, when you say things like "I don't want to have to find space to park yet another vehicle at home either", what most people do when they get a company car is to sell one of their other vehicles. You can almost always use your company car for personal reasons - you don't need to have more cars than you would otherwise want, just because one is company owned.
So the obvious answer is to ask when it comes to salary negotiation time. Then, if the company is OK with you not having the company car, decide if the extra money is worth it.