For undergraduate programmes, the cost of submitting an application is set by UCAS. For 2017 entry, if you are only applying for one course, the cost is £13. If you wish to apply to multiple courses the cost is £24. For more details please visit UCAS's website.
For postgraduate programmes, currently only Imperial College Business School charge an application processing fee for their postgraduate taught programmes. The application processing fee is £100 for MBA applications and £50 for MSc programmes. This fee covers the costs associated with processing your application. For more details, please read the Application processing fee terms and conditions.