Archerfield and Partners Solicitors had previously issued a statement confirming that they would take such action should the broadcaster not apologise by 5pm today.
Lawyer Mark Bateman has now said: "Following our earlier statement, we are deeply saddened that, despite requests, publicly-owned Channel 4 has not met the 5pm deadline for an apology over the deeply offensive and hurtful sexual comments it broadcast about Katie Price's disabled son Harvey.
"Accordingly, on Katie Price's instructions, we can confirm that we have had no option but to formally complain to Ofcom on Harvey Price's behalf about the comments."
On Tuesday night's programme, Boyle had joked: "Jordan and Peter Andre are still fighting each other over custody of Harvey - eventually one of them will lose and have to keep him."
He later added: "I have a theory about the reason Jordan married a cage fighter - she needed a man strong enough to stop Harvey from f**king her."