Yes, Cartwright-Hignett Partners holds a UK sponsor licence

It is on the Home Office register of licensed sponsors for the Skilled Worker route.

Licensed routes

Skilled Worker
A ratingWorker
For eligible skilled jobs in the UK. The role has to meet the skill level and salary rules for the route.
Read the route guide Check the salary rules

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 Cartwright-Hignett Partners assign one.
An A rating means Cartwright-Hignett Partners can assign Certificates of Sponsorship.
Being on the register does not mean Cartwright-Hignett Partners 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 Bradford-On-Avon

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.