Barker, the world No26 from Upminster in Essex, despatched fellow left-hander Mansoor Zaman, of Pakistan, 11-9, 11-7, 11-4 in 35 minutes, while Londoner Grant, the world No17 now based in Halifax, Yorkshire, defeated compatriot Joey Barrington, from Somerset, 11-10 (2-0), 11-5, 8-11, 11-8 in 57 minutes.
Long-time local Nottingham hero Simon Parke failed in his bid to earn a 14th appearance in the sport's most prestigious event. The 34-year-old Yorkshireman from Leeds – a former world No3 – battled for 46 minutes against Ong Beng Hee before bowing out 11-7, 11-7, 11-8 to the world No14 from Malaysia.
Welshman Alex Gough, also a former Nottingham stalwart, is now one place away from a tenth appearance in the PSA Tourevent in which he has made the quarter-finals on three occasions. The 35-year-old from Fleet in Hampshire dropped just two points against Daryl Selby before the 23-year-old from Essex was forced to retire with injury with the score at 11-1, 11-1.
Gough now faces Australian international Stewart Boswell, who beatEngland'sLee Drew, from Colchester, 11-5, 11-3, 11-7.
Domestic interest is being led by three English players in the women's qualifying event. Essex's Lauren Briggs claimed the swiftest second round win of the day, while Harrow's Dominique Lloyd-Walter survived the longest – and the pair now meet each other for a place in the main draw.
Briggs, the world No25 from Chingford in London, crushed France's Soraya Renai 9-3, 9-1, 9-2 in just 22 minutes.
In what turned out to be the longest ever match in her career on the WISPA World Tour, Lloyd-Walter battled to a 9-3, 9-3, 6-9, 7-9, 9-0 win over Canada's Runa Reta in an 84-minute marathon.
Rebecca Botwright is one match away from the chance of joining her illustrious sister Vicky Botwright in the main draw of the Dunlop-sponsored championship. The 24-year-old from Manchester beat Denmark's Line Hansen 9-2, 9-2, 9-5 and now takes on world No17 Annelize Naude after the Netherlands player overcame England's Sarah Kippax, from Cheshire, 9-1, 9-2, 8-10, 9-7 in 54 minutes.
Interestingly, the winner of this qualifying final match could face Botwright senior, the world No5, in Friday's first round.
RESULTS: Dunlop British Open Squash Championships, The University, Nottingham, England
Men's 2nd qualifying round:
Ong Beng Hee (MAS) bt Simon Parke (ENG) 11-7, 11-7, 11-8
Davide Bianchetti (ITA) bt Aamir Atlas Khan (PAK) 11-6, 11-7, 6-11, 10-11 (0-2), 11-4
Mohammed Abbas (EGY) bt Joseph Kneipp (AUS) 11-6, 11-7, 11-5
Laurens Jan Anjema (NED) bt Alister Walker (ENG) 11-5, 7-11, 11-9, 11-10 (2-0)
Peter Barker (ENG) bt Mansoor Zaman (PAK) 11-9, 11-7, 11-4
Adrian Grant (ENG) bt Joey Barrington (ENG) 11-10 (2-0), 11-5, 8-11, 11-8
Alex Gough (WAL) bt Daryl Selby (ENG) 11-1, 11-1 ret.
Stewart Boswell (AUS) bt Lee Drew (ENG) 11-5, 11-3, 11-7
Women's 2nd qualifying round:
Natalie Grainger (USA) bt Georgina Stoker (ENG) 9-5, 9-3, 9-4
Tegwen Malik (WAL) bt Laura Hill (ENG) 9-4, 9-6, 9-4
Dominique Lloyd-Walter (ENG) bt Runa Reta (CAN) 9-3, 9-3, 6-9, 7-9, 9-0
Lauren Briggs (ENG) bt Soraya Renai (FRA) 9-3, 9-1, 9-2
Manuela Manetta (ITA) bt Tricia Chuah (MAS) 9-6, 4-9, 9-7, 10-8
Isabelle Stoehr (FRA) bt Jenna Gates (ENG) 9-2, 9-0, 9-3
Rebecca Botwright (ENG) bt Line Hansen (DEN) 9-2, 9-2, 9-5
Annelize Naude (NED) bt Sarah Kippax (ENG) 9-1, 9-2, 8-10, 9-7
Men's Qualifying final line-up:
Ong Beng Hee (MAS) v Davide Bianchetti (ITA)
Mohammed Abbas (EGY) v Laurens Jan Anjema (NED)
Adrian Grant (ENG) v Peter Barker (ENG)
Stewart Boswell (AUS) v Alex Gough (WAL)
Women's Qualifying finals:
Natalie Grainger (USA) v Tegwen Malik (WAL)
Dominique Lloyd-Walter (ENG) v Lauren Briggs (ENG)
Isabelle Stoehr (FRA) v Manuela Manetta (ITA)
Annelize Naude (NED) v Rebecca Botwright (ENG)
The 2006 Dunlop British Open - featuring world-class men's, women's and masters events – gets underway with main draw first round action on Friday, leading to finals on Monday (18 September).