That figure could rise higher this month due to a surge in World Cup-related messages.
An MDA spokeswoman said: "Texting has become second nature to UK mobile phone users, with many bank holiday arrangements being made via text."
More than 120 million text messages were sent on FA Cup final day, rising to 124 million texts on Champions League final day.
A predicted 36.5 billion texts will be sent by UK mobile phone users this year - up from 32 billion in 2005, according to the MDA.