Kent and Hampshire secured qualification for the knockout stages of the Royal London One-Day Cup following their respective victories over Gloucestershire and Glamorgan.

Nottinghamshire, Worcestershire, Warwickshire, Surrey and Essex all kept their hopes of reaching the next stage alive, while Derbyshire’s defeat to Lancashire leaves them needing to win and rely on other results in the final round of fixtures.

Kent’s seven-wicket victory against Gloucestershire was their fifth in succession in the One-Day Cup and was largely inspired by centuries from Heino Kuhn (113) and Joe Denly (109 not out) in their pursuit of 323, which came with 21 balls to spare.

Kuhn and Denly shared a second-wicket partnership of 186 in Beckenham, strengthening Kent’s grip on second place in South Group and keeping their hopes alive of overhauling Hampshire and securing a bye to the semi-finals.

Gloucestershire now require victory over Middlesex on Wednesday and other results to go in their favour to secure a top-three finish. They had earlier recorded 322 for eight, with George Hankins scoring 92 from 120 balls.

Hampshire remain top of South Group after they secured a four-wicket victory over Glamorgan at Swansea.

An unbeaten stand of 85 between Brad Taylor (54) and Gareth Berg (52) saw them reach their target with 40 balls to spare for six after Glamorgan were dismissed for 227.

Hants will earn a home semi-final if they overcome Somerset in their final fixture on Wednesday.

Surrey’s hopes of reaching the knockout stages remain slim, despite them beating Middlesex by five wickets at Lord’s.

Last year’s runners-up reached their target with 11 balls to spare after dismissing the hosts for just 234, and now lie a point behind the third qualification place being occupied by Essex.

They need a victory over Glamorgan on Wednesday to be complemented by Essex losing to Kent and Somerset failing to overcome Hampshire.

Essex’s hopes of progressing were maintained with a four-wicket win against Sussex.

Tom Westley and Adam Wheater both made half-centuries in the successful pursuit of 282, with 12 balls to spare.

Laurie Evans’ 107 not out off 117 balls had taken Sussex to 281-7.

In the North Group, holders Nottinghamshire had skipper Steven Mullaney to thank as they stayed on course for qualification with a 31-run win against Durham.

Mullaney hit 124 as he rescued his side from 73 for five to 255 all out.

Durham were 177 for three in response but Mullaney removed Michael Richardson (68) and Stuart Poynter, which led to the hosts collapsing to 224 all out.

Victory on Thursday against Derbyshire would likely see Notts progress, but a defeat would definitely end their campaign.

Derbyshire could have been going into the game a point ahead instead of behind had they not lost by 25 runs against Lancashire.

Derbyshire now need a victory and hope Yorkshire fail to win one of their remaining two games to qualify.

Callum Ferguson’s 159 inspired leaders Worcestershire to overcome Northamptonshire by 34 runs at New Road.

Ferguson shared a club-record second-wicket stand of 239 with Joe Clarke (122) as the hosts recorded 348 for five, before bowling out Northants for 314.

Victory sets up a winner-takes-all clash with second-placed Warwickshire on Thursday, though both will already have qualified if Yorkshire lose to Lancashire on Tuesday.

Warwickshire secured a nine-wicket victory over Leicestershire, who were bowled out for 207.

Jonathan Trott’s 102 not out – his second century in three days – and an unbeaten 69 from Sam Hain then took them home with 12.2 remaining overs.