Wood - the former Joe Public Relations chief brought in last June as figurehead for Seventy Seven - has left without a job to go to.
The agency was launched to lure consumer brand PR work into FH, which has a mainly corporate reputation.
FH chairman Neil Hedges told PRWeek: 'We have agreed to part company.
It wasn't working out on both sides; it's one of those things and we're sad all round.'
Both Wood and Hedges insisted there had been no row. Wood said he had become increasingly interested in 'opportunities in integrated marketing', such as the work undertaken by FH's parent ad agency AMV BBDO.
Wood's heart is thought to lie more in such work, rather than the corporate PR/CSR activity that Seventy Seven has recently unsuccessfully pitched for, such as Starbucks and Birds Eye.
Wood is also believed to have wanted more autonomy than his role allowed.
Hedges has already appointed director Guy Corbet as MD, to succeed Wood.
Hedges said: 'Guy has earned the right to take up the mantle - Seventy Seven is very much its own agency.'
He said Seventy Seven had an 'extremely good' start, with annualised fee income already estimated at around £750,000 and clients such as eBay and Lycos.