London were relegated from Super League after Wakefield secured a 19-10 victory which preserved their top-flight status at the Broncos' expense.
Danny Ward's men began the evening level on points with Hull KR, Huddersfield and Wakefield but in bottom place due to their inferior points difference.
Hampshire scored again five minutes after the restart and then Reece Lyne added a third to confirm victory which sent the Broncos, who scored late consolations tries from Alex Walker and Brock Lamb, back to the Championship after one season back in the top flight.
The relegation rivals went set for set during the opening quarter as try-scoring opportunities were scarce.
Brough converted a penalty from in front of the posts to make it 2-0 but moments later London advanced up field and Trinity prop Craig Kopczak knocked on 10 metres from his own line.
That led to a spell of London pressure which saw them awarded a penalty against Danny Kirmond for holding down, but winger Kieran Dixon sent his conversion attempt wide.
In the 16th minute, the Broncos went close in the right corner when Lamb's flighted kick was narrowly missed by Dixon.
Three minutes later, London survived at the other end when Brough's last-tackle kick to the right corner was grounded by Ben Jones-Bishop, but the winger knocked on and no try was awarded.
At the other end, London earned a goal-line drop-out when Walker latched onto Lamb's high kick which came to nothing.
Wakefield began to look more dangerous and claimed the opening try in the 24th minute when Jacob Miller's kick to the left corner was expertly fielded by Hampshire.
He found team-mate Morgan Escare inside him and the Frenchman's reverse pass then sent Hampshire over the line for a try which Brough improved to make it 8-0.
London thought they were off the mark in the 38th minute when Walker's short offload sent Ryan Morgan over the line but the pass was forward and no try was awarded.
That ensured Trinity led 8-0 at half-time and five minutes after the restart they struck again.
After forcing London into a goal-line drop-out, Wakefield worked the ball out to the left flank where Hampshire collected Miller's long pass and touched down.
Brough converted to make it 14-0 and in the 52nd minute, London had their best chance yet when Dixon almost grounded a kick in the right corner but narrowly failed to do so.
Wakefield soon advanced up field and scored a third try when Brough's clever grubber kick was touched down by Lyne before London hit back with tries from Walker, who forced his way over in the right corner, and then Lamb in the closing stages.
Brough also landed a drop-goal for Trinity in a seven-point haul with the boot while Dixon kicked one conversion for the visitors.