Chief executive Andrew Finding contacted H&H to start the ball rolling.
In a letter to H&H he said: “Our 18 athletes won 16 medals – 67% took home one or more gold medals.
“Let’s now campaign for the Olympic and Paralympic team, as one, to win.”
The team award is given to the British team that “has achieved the most notable performance in British sport”.
At Greenwich, Team GBR’s dressage riders won historic double gold, the showjumpers scooped the first team gold for 60 years and the eventers took team silver.
The Paralympics saw riders win medals in every category for the first time and Sophie Christiansen won three gold medals.
With a crowded field for the individual SPOTY title – cyclist Bradley Wiggins is the bookies’ favourite at 4-6 – the team award may prove more fruitful for riders.
A BBC spokesman told H&H that the current selection system was
She said: “For the past few years, the individual and team contenders have been selected by sports editors on national newspapers and magazines.
“After last year [when there was an outcry over the all-male shortlist] we pledged to look at the entire system.”
The BBC would be able to give more details in October, she added.
Last year’s team award went to England’s Test cricketers, but equestrians have done well in the past.
Team GBR’s eventers won the award in 1972, following their double gold at the Munich Olympics, while the showjumpers won in 1979 and 1984.
And in 1981, the award went to the Grand National pair who triumphed over adversity – Bob Champion and Aldaniti.
But the SPOTY team award of 2000 could give an indication of this year’s likely winners.
It was at the Sydney Olympics that Britain began to climb the medal table – and, in recognition, the award went to the entire Olympic and Paralympic team.
This news story was first published in the current issue of H&H (27 September 2012)