The unmarked Harry Jeffries converted a corner from close range in the seventh minute, a lead Brock might have extended before the break as Hammers struggled to defend set pieces.
Martin Warren spurned United’s best chance of the first half, while the hard-working visitors stood up manfully to spells of second-half pressure before visiting winger Will Tickle was sent off for a second bookable offence eight minutes from time.
Dominic Allen’s free kick drew a fine save from Sam Cousins in the latter stages and with a minute to play, Hamworthy substitute Ben Osborne inadvertently blocked a certain equaliser from one of his team-mates.
But the game was up when Brock striker Daryll Phillips scrambled home a deep cross at Dan Ackerman’s near post, consigning Kemp’s charges to back-to-back defeats from their opening two Wessex League Premier Division matches.
United’s manager told the Daily Echo: “It was the same old story, the two goals we gave away were awful and we gave ourselves the problem of chasing the game again.
“When you can’t keep clean sheets it gets a bit desperate and we have to get the basics right. It’s alright working on passing and playing with a tempo but the back four’s initial job is to keep a clean sheet.
“Brockenhurst showed more desire in their defensive third than we did. Every time we looked like pulling the trigger they threw bodies in the way.
“We took the game to them and created the majority of the chances second half. I thought we were going to get an equaliser but we got caught in the last minute with another poor goal.
“They didn’t really open us up too much but they have scored twice. It’s getting repetitive and I’m bored saying it.”
Hammers: Ackerman, Yelland, Legg, Donachy, Haysom (Martin, 55), Blackburn, Allen, Hubbard, Cook, Warren (Osborne, 82), Hester. Unused subs: Cole, Penny, Pidgley.