Before Brexit, the UK could manage the national market competition under the implementation of EU competition law. At the same time, the UK competition regime contributed to the modernisation of EU competition law, which is the shift from the form-based approach to the effects-based approach. Since the UK left the EU, the UK Competition and Markets Authority (CMA) has shown its efforts to develop its competition law and policy on the digital economy, which indicates its independence from the EU competition regime. In particular, the CMA has published a number of reports of market study, including ‘Online platforms and digital advertising’ in July 2020. Moreover, the CMA has opened an investigation into Google’s Privacy Sandbox that has the proposals to remove third party cookies and other functionalities from Google’s Chrome browser. In effect, the European Commission also announced its investigation on the similar case. Therefore, it is meaningful to discuss the CMA’s approach to the digital advertising, which will be useful when we compare it with the EU’s approach. Then, it would be possible to find a level of convergence between the UK and the EU in competition law enforcements in the digital sector. In particular, the recent discussions on the business models in the ad tech become important. Since the German Facebook case, critics have asserted that the infringement of privacy should be regarded as an exploitative abuse. On the contrary, Google’s Privacy Sandbox plan aims to protect privacy (i.e., to avoid any possible exploitative abuse or data protection rule), but competition authorities, including the CMA, consider this privacy protection policy as an exclusionary abuse. In effect, Privacy Sandbox may be necessary from data protection regulation perspectives. The application of competition law to Privacy Sandbox may conflict with the rule of data protection law. In sum, there are notably complex conflicts and overlaps between the objectives of an exploitative abuse rule and an exclusionary abuse rule and between competition law and data protection law. This can be regarded as a ‘privacy protection paradox’. Moreover, the complicated framework in the ad tech of open display advertising market has brought discussions on the foreclosure by large gatekeepers in the vertically integrated structure. This issue involves the case of Privacy Sandbox. Lastly, it is also important to discuss the future of UK competition regime. The concept of Ordoliberalism, which heavily affects the formalistic approaches in unilateral conducts, continues to influence the development of EU competition law and policy. The idea of social market economy, relating to Ordoliberalism, is clarified in Article 3 of the Treaty on the European Union as an important value and goal of the EU. However, the UK does not have to accept these notions in the implementation of competition rules as the regime left the EU. Whether the UK competition regime continues to accept the concept of special responsibility that is from Ordoliberalism and social market economy will be one of the important topics after Brexit. This article aims to discuss the CMA’s recent approaches to the digital advertising sector, focusing on the Privacy Sandbox, thereby forecast further developments of the UK competition regime.