During the second world war there were no 'HEAD OF THE RIVER' records
but there were four unofficial BOAT RACES -

1940: UNOFFICIAL BOAT RACE at Henley - Cambridge by 9 lengths

Not even unofficial boat races in 1941 and 1942

1943: UNOFFICIAL BOAT RACE at Sandford (below Oxford) - Oxford by 2/3 length. See Boat race 1940s

In 1943, the second Wartime Boat Race between the Universities of Oxford and Cambridge was held on the Thames at Sandford. Like the first, it was unofficial and no Blues were awarded.
However, public enthusiasm was high and the river banks were thronged with spectators, all of whom had to reach the course either by bicycle or on foot. Contemporary newspaper reports estimate the crowd at between seven and ten thousand.
The Cambridge crew, unusually for the time, included a Dane at bow and a Turk at number four. The Oxford crew included four medical students.
The race was rowed between the narrow banks of the 1¼ mile course from Black Bridge (Nuneham Railway Bridge) to the island by Radley College Boathouse. Oxford won the toss and chose the Oxfordshire bank, with Cambridge rowing on the Berkshire side.
Oxford set off at 40 strokes compared to Cambridge's 37, and were almost immediately in the lead and a length up in some thirty seconds. Despite being left at the start, Cambridge did not give up and responded well, with the judge’s verdict at the finish recorded as a win for Oxford by just two-thirds of a length.

1944: UNOFFICIAL BOAT RACE on the River Great Ouse - Oxford by ¾ length

Cambridge led at the start and got a third of a length advantage, which they held for some distance, but as they approached Day's farmhouse Oxford began to draw up and then another spurt put them in front. Nearing the finish, Cambridge tried to spurt, but Oxford responded so that the Light Blues never looked like getting on terms again.

The Twelth Man's Sport Gossip, Monday February 28th, 1944 -

All things considered, I suppose the weekend Varsity boat race will go down in rowing history as about the 'strangest' in the whole series extending over 113 years. Again rowed far from its old peace-time home on the Thames tideway, this time in the very heart of the Fen country, on an isolated stretch of the Great Ouse, it still drew thousands of spectators, a great tribute to the hold the race has on the nation. They came not only from the cathedral city of Ely, but from Cambridge, military and Air Force units and surrounding villages. All manner of transport was used - lorries, horses, a few cars, bicycles (push and motor), and Shanks's pony involving miles of foot slogging.
Convalescent airmen filled a hastily improvised grand stand of chairs set out on the tow path right opposite the winning post, American troopers gathered on banks behind and Australian airmen filled in points of vantage. The whole show was free, but one bank of the river was reserved for those who had official cards of the race, issued by Cambridge University B.C. When these gave out - there were only about a hundred printed - the county police had to give way, so great was the crush.
Everyone who got to the race regarded it as distinctly an occasion - and favours were worn. As the race was staged on Cambridge waters, light blue naturally predominated. But some prophetic soul had planted an Oxford blue flag to mark the finishing post in front of a step ladder, presumably for the finish judge, the Rev M H Tupper, an old Oxonian, to mount at the psychological moment, but I do not recall that official finding this necessary. With the bar up against launches (on points of speed and wash), the umpire, Captain Stevenson, followed the race on horseback, as did the coaches.
Another innovation - for the Varsity boat race - was the timing of the race from the winning post, over a telephone line rigged up for the occasion by the Cambridge University Senior Training Corps signals, with the help of local Home Guard, to the starting point of the race. The actual man who held the watch in one hand and a telephone receiver in the other listening for the "are you ready, row" was A Cameron, of Pembroke, a member of last season's Cambridge crew.
The crews were not ready when the hour of starting came. "A lump of mud was discovered," one of the oarsmen told me afterwards, that meant the stake boats being discarded and a few yards cut off the length of the race. But the race was the thing, and that provided a great struggle with Cambridge leading by a canvas until half way, where Oxford went ahead to just keep their lead to a great finish. The better crew won, making themselves favourites for the race when they paddled down from Ely past the crowd to the starting point down the river close to Littleport.
This very youthful boat race crowd, full of servicemen, about 5000 strong, against the millions who lined the Thames banks in peacetime, reproduced the typical humour of the old gatherings. They were, for an instance, much amused, while waiting for the crews to hove in sight, by the manoeuvres on one of the banks of a young man with a portable wireless set. He kept on proclaiming himself to be 'Z for Zebra' to the intense delight of the convalescent airmen, who cheered with great gusto everything he said.
One of the winning crew told me afterwards how amused he was by the mock booing and hissing of people on the banks (nearly all staunch supporters of Cambridge, the home side) as his crew paddled down to the starting point. But these same people, as I reminded him, gave the dark blue winners a great reception at the finish and joined in the cheer which the beaten crew, as usual, gave for their conquerors. Then the crews paddled back to the Ely boathouses to have tea in town and later dine (at a Cambridge hotel) together, as they had lunched at an Ely hotel before the race. I fancy the losers paid.
None of the American soldiers at Ely had ever seen the race before and naturally knew little of its standing in this country or long history. One who came from Utah, intrigued me by suggesting that there ought, "To be more boats in the race," adding "But perhaps it was some sort of final!" But even he was very impressed by the racing and voted it "Swell."

Boatrace on the Great Ouse, 1944

The Diamond44 re-enacted the 1944 race in 2004. Cambridge won by 4 lengths.

1945: UNOFFICIAL BOAT RACE at Henley - Cambridge
British Pathe film of 1945 Boat Race

1946: 92nd BOAT RACE - Oxford by 3 lengths. Oxford 43, Cambridge 48. See Boat Race 1940s
In this race Cambridge had used swivels and Oxford had fixed thole pins.
1946: HEAD OF THE RIVER - Trinity

1947: 93rd BOAT RACE - Cambridge by 10 lengths. Oxford 43, Cambridge 49. See Boat Race 1940s
1947: HEAD OF THE RIVER - Trinity

1948: 94th BOAT RACE - Cambridge by 10 lengths. Oxford 43, Cambridge 50. See Boat Race 1940s
1948: HEAD OF THE RIVER - Trinity

1949: 95th BOAT RACE - Cambridge by ¼ length. Oxford 43, Cambridge 51. See Boat Race 1940s
This was the first race to be covered by television:

1949. The Consuta set up to carry the television camera and crew

This was the famous race in which John Snagge, commentating for the BBC, overcome with excitement, uttered the memorable words -

I can't see who's in the lead - it's either Oxford or Cambridge.

1949: HEAD OF THE RIVER - Trinity

In 1949, after ninety five boat races, the overall tally was: Oxford 43, Cambridge 51 (and one dead heat) The war time unofficial races are not counted. Leadership in Overall Tally of Boat Race Wins:

1829 1949