Ok, I’m married with wife working and two children with my own car!
How much if any tax credits your wife has left over could have an impact, or the other way around, if you have any tax credits left your wife could use them, or if you were unemployed and your wife was using your tax credits and higher rate extension she may earn less.
You car will have 0 affect, you would pay less tax if you were buying annual taxsaver bus tickets or bought a bike through work.
Your kids might have an impact, especially if you are paying college fees or medical expenses for them.
Put your details into a tax calculator for 2020, your employer pension contribtion is 0% your contribution is 3%.
Just note too, some office don't have parking, some have limited parking and it can be awarded based on seniority, a waiting list, a raffle, applying weekly for a permit, or probably some other ways, some have ample parking but that's rare.