in 2021[1] a Supreme Court ruled that their drivers are employees (and not self-employed people), so I suspect the invoice shall be coming from the company. Perhaps that's also why HMRC is pursuing the VAT for the past year or two.
The court found they were "workers" rather than employees. It's a sort of half-way status in English employment law for people who are neither employees nor self-employed. It provides some, but not all, of the rights of employment. Most relevant here, it guarantees minimum wage.