An exit from the EU would have limited impact as far as the EU antitrust rules are concerned (Article 101 TFEU on anti-competitive agreements and Article 102 TFEU on abuse of a dominant position), because these rules apply equally to non-EU companies who carry on business in Europe or whose activities affect trade in Europe.
In addition, the UK competition rules (the Chapter I and Chapter II prohibitions of the Competition Act 1998) completely mirror the EU antitrust rules and businesses are therefore subject to a very similar regime where conduct has an impact in the UK only. However, one impact of a UK exit from the EU would be that there will be many more cases where both the EU and the UK could in parallel open an investigation and impose fines and other remedies for anti-competitive conduct affecting both the continuing EU and the UK. While the UK is within the EU it cannot investigate where the EU Commission takes jurisdiction. This could potentially add to risk and costs for affected businesses.
In respect of merger control, again the impact of an exit is likely to be parallel investigations. The EU Merger Regulation (EUMR) introduced a so-called one stop shop regime, under which a transaction that qualifies under the EUMR is no longer subject to the merger control regime(s) of the relevant Member State(s) (subject to some exceptions). If the UK is no longer a Member State, the EUMR and UK merger control regimes would run in parallel. A transaction that qualifies under the EUMR may also be subject to UK merger control (provided the jurisdictional threshold for UK merger control is met). This could add a burden and cost for businesses, in particular in view of the level of the UK merger fee (ranging from £40,000 to £160,000 depending on the UK turnover of the enterprises acquired) and the longer time frames for UK merger control clearance.
If the UK were to join EFTA and the EEA, a third body, the EFTA Surveillance Authority, would have jurisdiction over certain mergers (e.g. a merger of energy businesses operating only or largely in Norway and the UK).
On the other hand, unless the UK joins EFTA, EU State aid rules would cease to apply in the UK and only somewhat more limited rules in the WTO agreement would apply. This is a sovereignty related issue and the UK government would likely choose to keep any flexibility gained from this change.
The same structural outcome applies to public procurement rules. However, the UK currently has quite stringent procurement rules of its own supplementing the EU regime and might chose to adopt its own public procurement rules and enforcement regime closely based on current EU law.