This is an ordinary consumer-rights situation, since the facts you describe do not bring in certain other legal rules that might apply for cosmetic treatments -
- I assume you are over 18. If you are not, and the treatment was one of those mentioned in the Botulinum Toxin and Cosmetic Fillers (Children) Act 2021, then there may have been a criminal offence committed by the person giving the treatment - depending on the circumstances.
- If this were a surgical intervention, then there is a particular legal regime about practitioner standards and complaints. The principal act is the Medical Act 1983 but there are plenty of other related laws. From the way you describe it, it sounds like it was non-surgical, the kind of thing which can be done by somebody who doesn't need to be specially licensed and qualified as a surgeon. For better or worse, cosmetic treatments like fillers aren't considered to be medical in this way.
- If this happened in the National Health Service, as opposed to a private setting, then there are are specific processes about complaints and so on - not necessarily statutory in nature, but the point is that you can't really complain to the NHS about something where they weren't involved.
- If you had been physically harmed by the procedure, as opposed to feeling that it did nothing at all except waste your time and money, then there are all sorts of other civil and criminal possibilities you might be able to pursue.
For your consumer rights, the main place your statutory rights are set out is the Consumer Rights Act 2015, and see especially its Part 1 Chapter 4 on services. This legislation consolidates previous UK laws on the topic. It frequently refers to the Consumer Contracts Regulations 2013, which is the statutory instrument implementing the EU Consumer Rights Directive of 2011.
Although these consumer rights are UK-wide, there are different bodies you can go to for advice and advocacy depending on where you are - see the government's Consumer rights contact page. The rights and remedies described here are a bit abstract, because they cover many different kinds of services: in a specific case a lot will depend on what's reasonable for the service involved, which won't be set out in statute.
What you'll see in the legislation is that there are some outcomes you can hope for, including a partial or full refund, or that they would have to repeat the treatment at their cost. Whether you are able to achieve that hope is the question. The text of the Act shows that things depend on how they described the effect and costs of the treatment. I see that there is some disagreement between you and the clinic about what they said in the initial consultation, and this is exactly the sort of thing that is important when it comes to your rights - whether the service they provided was as described, or not. A lot of the detail in the law is about discerning that boundary in how the terms should be communicated, dealing with estimated costs versus actual costs, the possibility of the treatment not working or having adverse effects, and so on. There are some rights that don't apply here, such as the 14-day period for cancelling an ongoing services contract because you changed your mind - that time has now passed.
The relevant advocacy body from the link above would be able to help you figure out your next steps.