Ofcom announced last week that it has opened separate investigations into Vodafone and Three.
"Traffic management practices" deployed by both companies are under scrutiny as part of the probe, including their alleged "throttling" of certain types of internet traffic when customers are roaming.
A Three spokesperson said the company would be "working closely with Ofcom to understand their concerns".
Vodafone said it was "very disappointed" with Ofcom's decision to "target" its 'Vodafone Passes' service, where customers can access services from content providers without it impacting on their data allowances.
In a statement, a spokesperson for Vodafone said: "Our Passes allow customers to access their favourite content without fear of running out of data or attracting out of bundle charges. They are open to any content provider of video, music, chat and social. 22 content providers have signed up so far, ensuring Vodafone customers can enjoy the widest selection of worry-free access to content across the industry."
"Vodafone does not 'throttle' speeds on Vodafone Passes, either in the UK or while customers are roaming. The Video Pass is optimised so that all of our customers have a high quality experience when streaming content on the network. Optimising means making the bandwidth available that enables videos to be delivered in a faster, more efficient way, while still providing the best smartphone viewing experience, and without compromising the experience of other customers who do not use a Vodafone Pass," they said.
"We developed Vodafone Passes in direct response to customer feedback and have provided clear information to customers about how they work. We will be explaining all of this to Ofcom during the course of their investigation," the statement said.
EU net neutrality laws that came into force in April 2016 give internet users the right to "access and distribute information and content, use and provide applications and services, and use terminal equipment of their choice, irrespective of the end-user’s or provider’s location or the location, origin or destination of the information, content, application or service, via their internet access service". Internet service providers (ISPs) must "treat all traffic equally".
Notwithstanding those requirements, however, the regulations permit ISPs to implement "reasonable traffic management measures" which are "transparent, non-discriminatory and proportionate", such as blocking or throttling the delivery of content requested by users of their network, for reasons such as preserving the integrity and security of the network or combatting network congestion. Where they deploy traffic management measures they must be open about it with customers.
Ofcom announced in December last year that it was looking into the way ISPs in the UK manage network traffic. The regulator said it intends to provide an update on its investigations, and other work in this area, by June.