Boreham Wood walked away with all three points at the Shay Stadium after a tap in from Josh Rees.
Bradbury produced a smart block in the 7th minute to deny Josh Rees the opener.
Boreham Wood took on their first shot of the game just a minute later when Frankie Raymond’s shot from outside the box was fired straight at Sam Johnson in the Halifax net.
At the quarter hour mark Josh Rees was so close to finding the opener for Boreham Wood but his scuffed shot from inside the 6-yard box beat Johnson but couldn’t beat Jesse Debrah who cleared the effort off the line.
Towns first chance of the game came when Harvey Gilmour had two shots from the edge of the box, the first blocked and the second attempt which flies over the crossbar.
In the 28th minute Gilmour was causing more problems for Boreham Wood when he took on a left footed finesse shot from outside the box which was well blocked in the end.
Just 4 minutes after and the Shaymen had another double attempt through a blocked Warburton shot and then a well hit shot from Martin Woods which fell just wide of the post.
37 minutes in and Boreham Wood found the lead through Josh Rees. Some clever play on the left-hand side from Jacob Mendy left Jay Benn stranded before squaring the ball to Rees who slotted home past Johnson. That was to be Rees’s 6th league goal of the season and his second against Town.
3 minutes before half time Mendy was twisting and turning again outside the box before eventually firing high and wide.
In added time David Stephens committed a foul on Jack Senior that left Town with a good position to shoot from the free kick. Matty Warburton too the free kick which was well saved to his left-hand side from Taye Ashby-Hammond.
Halifax Town started the second half brightly as Jay Benn found himself in a good position to shoot but ended up wide of the post.
In the 60th minute a cross was played into the back post which Jack Senior headed back across goal but no man in blue was there to finish off the attack.
Eleven minutes later Town defender Tom Bradbury tried to float the ball into the box which was headed away with ease before the ball fell to Matty Warburton who was trying to find space to shoot on the edge of the box but was disposed in the end.
Just after and a through ball was played in towards Matty Warburton who looked to be in on goal but some incredible recovery work from James Comley who got across well to tackle denied Halifax to opportunity to equalise.
With just nine minutes to go Town really started to pile the pressure on Boreham Wood as Town substitute Jamie Allen had a cross into the six-yard box cleared away.
Boreham Wood came very close to finding a second goal as Tyrone Marsh took a cross from the right-hand side that clipped the crossbar before bouncing out for a throw-in.
In added time Luke Summerfield fired in a teasing cross into the box but Boreham Wood did well to clear their lines.
Boreham Wood held on to take all three points and sentenced FC Halifax Town to two consecutive defeats for the first time this season. Town dropped down to 3rd while Boreham Wood remain 5th in the National League table.
FC Halifax Town: 1 Sam Johnson, 2 Jay Benn (7 Jamie Allen 74), 3 Jack Senior, 5 Jesse Debrah, 6 Tom Bradbury, 9 Aaron Martin, 10 Matty Warburton, 11 Billy Waters, 20 Harvey Gilmour (4 Luke Summerfield 63), 26 Martin Woods, 31 Niall Maher (21 Tyrell Warren 46)
Subs: 15 Gerry McDonagh, 16 Jamie Thomas
21 Taye Ashby Hammond, 5 Will Evans 6 David Stephens, 7 Josh Rees, 9 Scott Boden (19 Danilo Orsi 79), 10 Tyrone Marsh (14 Adrian Clifton 90), 11 Frankie Raymond, 12 Jamal Fyfield (2 Jamie Reckord 31), 16 James Comley, 17 Jacob Mendy, 19 Kane Smith
Subs: 23 Josh Roach, 15 Dennon Lewis
Referee: Thomas Parsons
Goals: Rees 37
Yellow Cards: Stephens 45, Woods 87, Comley 89
Attendance: 2256 (30 away)
FC Halifax Town 0 Boreham Wood 1
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