The Williams development driver became the first woman in 22 years to take part in a competitive Formula One grand prix weekend on Friday.
But the 31-year-old Scot had minimal involvement in the session as her car was stopped due to oil pressure problems.
Wolff's one flying lap at Silverstone saw her set a time of one minute and 44.212secs.
However, she was unable to improve on that mark as her car came to a halt, bringing her session to a frustrating conclusion.
"Really tough day but that's Formula One sometimes," Wolff told BBC Sport. "There was an oil pressure problem that cut the engine off.
"For me it was good to get that first run on an actual race weekend, now I can keep working towards working Hockenheim knowing what I have to do."
Wolff's problems were just the start of a bad day for Williams, who saw another one of their drivers fail to finish the session when Felipe Massa was sent spinning into the wall after misjudging a corner.
There will be another chance for Wolff to show her quality when she drives at the German Grand Prix at Hockenheim in two weeks' time.