There is no evidence for this.
The video supplies two sources: A Quilliam study and a police officer. Neither say that there are millions of rapes by Muslims, and the 222 convictions are not related to alleged rapes committed by Muslims.
Only 222 convictions
The given source is an unnamed Quilliam study. It is the study referenced here, which isn't about rape of children in general, nor about Muslims or illegal immigrants.
The organisation [...] said it found 222 of 264, or 84 per cent, of people convicted of specific grooming-gang crimes in the UK since 2005 were Asian.
There is doubt about the Quilliam findings:
Laced with contradictions, misrepresentations and blatant fabrications, the report also appears hastily thrown together, with paragraphs copied and pasted into multiple sections. Their statistics are pulled from incomplete research, and use a specific definition of ‘grooming gangs’ that is again different from the figures they cite from other studies. The report has been highly selective of not only the references it opts to use, but the specific sections of those sources it decides to include or omit.
Rotherham and millions of victims
The second source that is given in the video is a Rotherham police officer.
Rotherham is the place where a child sexual abuse scandal took place.
The police officer said:
We don't know for sure. But I think it's tens of thousands of victims [a year] of an appalling crime," Mr Bailey said. [...]
"[The] bigger picture is that 90% of child sexual abuse takes place in the home where crimes are being perpetuated upon victims by people they know already. It is really important that we get some context around this."
Using this as evidence of millions of rapes by Muslims makes no sense; the officer is talking about child sexual abuse in general, and that the perpetrators are overwhelmingly people the victim knew already.
tl;dr There is no evidence at all for millions of rapes by Muslims. The 222 convictions mentioned are related to "grooming-gang crimes", not rape of children in general, and thus do not show an inaction on the part of the UK in response to rape.