I'm afraid the VIP Fortress flight is unlikely to be discovered without ploughing through every record of every squadron...and even then it might not come out. Most published operational records only relate to combat operations and not individual VIP duties.
A faster approach might be to see what dignitaries were pootling around the UK in Jan 1944. One presumes it was an American visitor but there was also a Chinese delegation which visited later in January that might have a connection. It's also possible the B-17 was a personal transport for a senior officer. Ira Eaker, for one, used such an aircraft in the UK until 5 January 1945 when he took charge of the Allied Air Forces in the Mediterranean.
Below is what Eric Hammel writes about January 20, 1944 in his book 'AIR WAR EUROPA America's air war against Germany in Europe and north Africa, 1942-1945 Chronology'
Not much help to you either I'm afraid.
Unfortunately, back to the original question, we have no details of who the VIP might have been. We don't even know for certain that it was a USAAF B-17. It's much more probable that it was an American aircraft but there's still a chance that it was an RAF machine. I tried to find any reference to RAF B-17s being used for VIP work but nothing leapt out at me on the interwebbythingy.