Before you have a right to appeal, you would usually need to ask for the decision to be looked at again. DWP call this a "Mandatory Reconsideration," whereas HMRC call it a "Review." (If you need more information about this see here.)
If you're not happy with the outcome of the reconsideration, you can appeal to Her Majesty’s Courts and Tribunals Service (HMCTS). Your appeal will be heard by an independent tribunal called the "First-Tier tribunal."
Your decision letter will always tell you what your options are, i.e. whether or not you are eligible to appeal.