Depending on circumstances of the refusal, you may have the right to an administrative review of the decision, especially if you submitted a Points Based System application. An administrative review is a review of the same application and the same supporting documents that is carried out by a different Home Office official. It is vital to correctly identify the mistake the Home Office made and submit strong representations to request its rectification.
Judicial review is a remedy of last resort to challenge the decision of the Home Office which was so unreasonable that no reasonable person acting reasonably could have made it. When all alternative remedies have exhausted, it is possible to bring a claim for permission for Judicial Review.
Sometimes it may be an option to consider making a fresh application, which may be a quicker and easier, however, it might not always work in your favour. If your legal residency in the UK is affected by this, it may be more appropriate to submit any of the above forms of challenging the decision.