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I'm currently abroad and I was wondering if there was a way to recieve texts while abroad without activating mobile data?
Unless you are receiving a MMS message or sending and receiving a message through an application such as WhatsApp where it is necessary to use a data connection, mobile data is not used to send and receive text messages, texts messaging is sent and received over the mobile network. This means you can safely turn off your mobile data and just make sure you have a connection to the roaming network for your calls and sending and receiving texts messages.
Even when abroad it is free to receive calls and texts messages and you won't need to be concerned about charges.
Although you are abroad roaming, make sure the person sending the messages or calling uses the UK country code and drops the first 0. For example +447000000.
Please also see this link: Travelling Abroad