Nowhere near £20K. £250 for your ARDs, £5K for a Cat-D Zed, £200 for pads, £1K tops for suspension, £1500 - £2000 for cage & extinguisher & cutoffs, £500 for seat & harness, and then whatever you want to spend on safety gear but around £400 is doable for the minimum. Under £10K for a competitive car, sorted.
That said, you have to be prepared to write off the cost of the car if you bin it, plus body damage at each race, & the entry fees, tyres and timing bits at each race. That's where the costs quickly add up.