Does the High Court of Justice of England and Wales (Queen's Bench
Division) ever exercise original criminal jurisdiction in serious
cases (eg, a terrorism trial) in modern times? Has it ever exercised
such jurisdiction since its creation by the Judicature Acts?
No, with the exception of criminal contempt of court proceedings (which arguably don't constitute "serious cases").
Prior to the Constitutional Reform Act of 2005, the Lord Chief Justice of the High Court was "President of the Criminal Division of the Court of Appeal and Head of Criminal Justice, meaning its technical processes within the legal domain," but these duties were appellate and administrative in nature, rather than involving original jurisdiction, and under the 2005 Act the Lord Chief Justice can appoint another judge to these positions.
England's criminal courts and civil courts were already almost completely separated before the modern "High Court of Justice was established in 1875 by the Supreme Court of Judicature Act 1873." The High Court is a direct successor to courts dating all of the way back to the 1200s, some of which had original criminal jurisdiction, but those predate the Judicature Act cutoff of the question.
This said, English legal history is not a model of strict consistency, and I wouldn't be stunned to discover some random one-off original jurisdiction criminal trials in the late 1800s or early 1900s under statutes that have now been long since repealed that attracted little notice and have little or no modern legal importance. But, I have no actual knowledge of any such exceptions.
For example, while the Admiralty Division of the High Court is now exclusively civil, I wouldn't be stunned to discover that the Admiralty Division at some point long ago, but after 1875, might have had original criminal jurisdiction over crimes committed on the high seas, like piracy and mutiny, even though it no longer has such jurisdiction. England's Admiralty Courts historically had this jurisdiction, and England's Admiralty Courts were consolidated into the High Court in 1875. But it isn't easy to discern from the resources available to me precisely when authority for crimes committed on the high seas was transferred from England's Admiralty Court to the Crown Courts (which have jurisdiction over these cases now).
Similarly, while debtor's prison was abolished in England in 1869, a few years before the High Court was created, I wouldn't be shocked to find that the Queen's Bench division may have handled some residual original jurisdiction cases related to quasi-criminal body executions for non-payment of debts originally resulting in incarceration in debtor's prisons, in cases originally arising prior to 1869 that weren't fully wrapped up in 1875.
Some countries with common law legal systems and a court system based upon the English model have courts called a "High Court" which consolidate the functions of the English "High Court" and the English "Crown Court" (which handles trials in serious criminal cases) in a single court. This is frequently motivated by a shortage of judges with the exceptional legal competence necessary to inspire confidence in the conduct of such proceedings.
In U.S. practice, for example, it is the rule and not the exception, for felony criminal cases, civil cases arising in equity, serious civil cases arising at law, and both criminal and civil appeals from lower courts to all be handled by the same court of general jurisdiction (although the terminology, of course, is usually slightly different since the U.S. does not have, and has never had after 1776, a King, a Queen, or Lords, as a matter of constitutional law).