Yes, Suzuki GB Plc holds a UK sponsor licence

It is on the Home Office register of licensed sponsors for the Global Business Mobility: Senior or Specialist Worker and International Sportsperson routes.

Licensed routes

Global Business Mobility: Senior or Specialist Worker
A ratingWorker
For senior or specialist employees moving to a UK role from an overseas part of the same business.
International Sportsperson
A ratingWorker
For elite sportspeople and coaches endorsed by their sport's governing body.

What this means if you want to work here

To work for a UK sponsor you need a Certificate of Sponsorship from them before you can apply for your visa. A licence is what lets Suzuki GB Plc assign one.
An A rating means Suzuki GB Plc can assign Certificates of Sponsorship.
Being on the register does not mean Suzuki GB Plc is hiring, or that it will sponsor a particular job. Sponsorship is decided role by role, so ask before you apply.
The job itself has to qualify too. Licences are granted per route, so a role has to fit a route listed here and meet that route's skill and salary rules.

Look for open roles

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Other sponsors in Milton Keynes

Source: Home Office register of licensed sponsors. UK Sponsors is independent and not affiliated with the UK government. This page is a plain-English summary, not legal advice.