"I've been training really hard over the summer - endless bikes and swims for up to three sessions a day," explained the left-hander. "So much so, that I was looking forward to the start of the season so that I could stop training!
"Greg is a class act. But I needed to get myself fitter so that I could deal with his pace. In fact, I thought to myself as I went on court - 'I doubt he's done as done as much training as I have'!"
The 25-year-old world No8 will now meet England team-mate Nick Matthew after the fourth seed from Sheffield ended the giant-killing run of compatriot Daryl Selby.
The unseeded 26-year-old from Essex had reached the last eight after taking out two world top 16-ranked opponents - but world No5 Matthew was too strong, winning 11-7, 11-5, 11-8.
"I'm delighted to be playing Pete tomorrow," said Matthew, who in 2006 became the first home-grown winner of the title for 67 years. "We're sharing a room together here - I must pop something into his glass of water tonight!"
In the women's championship, Yorkshire's Jenny Duncalf went one step closer to reaching the final for the second year in a row after beating eighth seed Vanessa Atkinson, the former world champion from the Netherlands, 11-1, 10-12, 11-6, 11-4.
Fourth seed Duncalf will face three-time champion Rachael Grinham, the second seed from Australia who recovered from a game down to beat Lancashire's Laura Massaro 5-11, 14-12, 11-7, 11-7.
RESULTS: internationalSPORTgroup British Open Squash Championships, Manchester
Men's quarter-finals:
[4] Nick Matthew (ENG) bt Daryl Selby (ENG) 11-7, 11-5, 11-8 (48m)
[6] Peter Barker (ENG) bt [2] Gregory Gaultier (FRA) 11-7, 7-11, 11-3, 7-11, 11-8 (76m)
More to follow ...
Women's quarter-finals:
[4] Jenny Duncalf (ENG) bt [8] Vanessa Atkinson (NED) 11-1, 10-12, 11-6, 11-4 (39m)
[2] Rachael Grinham (AUS) bt [6] Laura Massaro (ENG) 5-11, 14-12, 11-7, 11-7 (54m)
More to follow ...