If you need a car to do your job and your colleague doesn't, then presumably you're not doing the same jobs - so equal pay doesn't come into it surely.

Is this for real.

Simple advice, negotiate a better salery come review time and if unhappy leave for a better job.

For the sake of this discussion please assume my contribution to the business is equal to theirs.

That's a big assumption.

In my former employment (public sector) we had pay scales with incredibly lengthy progression times. Two people doing same job could be £5k adrift in pay rates but a bright newcomer could, in a year or so, be as good as a 20 year stick in mud but latter was on several £k more per annum.

Absent scales etc OP needs to negotiate a significant increase in basic.

Depends what exactly is meant by Car allowance

For 15,000 miles per year the HMRC standard rate allowance would be £6,750

If you mean by 'car allowance' money in lieu of a company car, then yes, its just regarded as salary. Most companies will regard that as a perk for staff who are of a grade that, from time-to-time, needs to use a car on-the-job (going to meetings, site visits, etc) but probably doesn't do that much work-based (not including commuting) driving, e.g. if, like I did in my last job, about 2.5k business miles a year tops and most of my work-based travelling was by train into London.

I received about the same allowance (on a much higher salary), but then only received the 'fuel only' rate (far less than 40 or 45p per mile, which includes for depreciation, maintenance and replacement of the car) nearer to 15p per mile, based on my car's engine type and size (essentially their guess at my mpg). I personally didn't like what they did, but in the end I didn't get anywhere near the 2.5k miles a year anyway.

My 'car allowance' covered what the fuel rate did not, namely depreciation, maintenance and replacement of the car, which for me, owning an older (11yo at the time) but generally very reliable car, was quite lucrative, as depreciation on it is almost zero and maintenance is still quite reasonable.

If, on the other hand, you own a less reliable car that's about to go pop/fall apart, and you go for makes/models that are similarly unreliable/not long-lived/expensive to run, then, especially if you do a lot more business mileage and/or own a gas-guzzling performance car (particularly petrol-engined), then such an arrangement is not lucrative. Its then more cost-effective to get a company car (if you can) which you can use for the commute to work and business driving, and, if you want to keep your own flashy/beloved motor, just use it on weekends with a reduced annual mileage and insurance cost.

To determine what is useful for you, both from a cost and practical POV, then you'll need to do a cost analysis using whatever mileage (home and work), maintenance adn other running costs, replacement car thoughts and how much the firm will pay you for each option based on your likely usage. Additionally, if you go for a company car, then sell your own car, but down the line (worse if sooner) leave the firm, it means you may be seriously out of pocket due to having to buy a new car to replace the company one, hence you need to think about your future at the firm over the short and longer term, including chances of promotion or relocation that may affect salary and perks. Be also aware that some firms are (like mine was) VERY picky about what car you get - you may not even have a choice, or be able to get a new car at all (i.e.a 2yo second hand one). At least they pay for tax, maintenance and insurance, probably (check) including a partner/spouse.

My pension was also calculated in the same way - its the way that many firms get round paying higher salaries, because also bonuses are also based on the salary without the car allowance, which often goes up by less (if at all) than your annual pay rise, which could mean its effects are dimishing over time until you get promoted.