If the home office or the Entry clearance officer has refused your visa without the right of appeal then you can apply for Administrative Review.
The fee to apply for administrative review:
It will cost you £80.00 excluding the fees of the solicitor to apply for administrative review and you should apply within 14 days from the date of the refusal of your visa.
During this process, the Home Office will only look at the administrative error in spite of the point of error of law. If you are not successful in this process then you can further challenge it by way of Judicial Review.