Forming a limited company in the UK is relatively straightforward. It’s probably best if you start the process by visiting this part of the .gov.uk web portal.
Aside from this, you need to consider carefully the taxation aspects. You explain that the business operations will be in a number of overseas countries. As a UK resident company this could mean complex tax issues. You need to address the taxation aspects before you start the project. You should talk to a chartered accountant who is familiar with US taxation. They can also advise on forming a limited company and ensuring that the memorandum and articles allow the activities the company wants to undertake, as well as ensuring that the company complies with UK and US taxation requirements and the most appropriate corporate structure for the US operations. Your adviser needs to have a full understanding of the operations of the sporting event.