For undergraduate programmes, UCAS charges one rate for a single application and another rate for multiple applications. 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. Please note from September 2019 the application fees will be increasing to £125 for MBA applications and £80 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