How could Moriarty walk clean from the trial after breaking into three key places (S02E03)?

How is it possible that the jury be allowed to ignore an evidence as strong as video recording of a surveillance camera?

I dislike answering a question with another question, but in this case I think its warranted.

What would be the purpose of a jury if they were only allowed to convict and not acquit the accused?

In the case where the entire jury was persuaded to give a not-guilty verdict, I don’t think UK law would allow for a mistrial unless there were evidence of the pressure on the jury.

Yes, the UK does allow for non-jury trial in cases of jury tampering but these appear to be invokable in cases of mistrial, which would only happen in cases where the jury were unable to reach a verdict, or serious procedural problems in the trial. I don’t think this would include the jury simply not returning the expected verdict.

Normally in cases of jury tampering, it would be nearly impossible to tamper with the entire jury without one or more reporting it to the court. Persuading just one or two would typically just result in an unanimous verdict being impossible to reach.

However it is suggested that Moriarty is able to get to all the jury:

Sherlock: Got to the jury of course

Jim: I got into the Tower of London; you think I can't worm my way into 12 hotel rooms?

This of course plays into the mystique of Moriarty, that he is more than a typical criminal. If we assume that he can persuade all twelve jurors to acquit without revealing the pressure to the court, there is little that can be done.