Somewhere to Go If the Worst Happens
One of the biggest issues with unregulated providers of injectables is culpability. Unless you can show that you have been harmed by the procedure the definition of whether they have done their work well or not is very ethereal. There is no regulatory organisation and your only option would be a court claim which can be both inconvenient and costly.
However, any minor disputes at a dental clinic and the staff will do their best to resolve the matter in a satisfactory way, as maintaining the reputation of the surgery is far more important than that of a pop-up kiosk.
For serious issues with the quality of work, there is the General Dental Council who are responsible for maintaining the standards of dentistry in the UK. This includes any cosmetic procedures that occur at any dental clinic. They are responsible for maintaining a register of which dentists are permitted to practise and have a mandate to investigate all complaints and restrict licences to practise where appropriate.
You can easily get in contact with the General Dental Council via their website. Their dental register is also publicly available, allowing you to research the credentials of your dentist before any treatment.