Atrás
The in-form Dudeney extended her winning run to seven matches in the World Tennis Tour W100 event at Wrexham Tennis and Padel Centre, outlasting seventh seed Susan Bandecchi from Switzerland 6-3 6-7 6-4 in a match lasting two hours and 51 minutes.
She will now face French player Elsa Jacquemot in the last eight.
Dudney was followed into the Carden Park Arena by Klugman, with the 17-year-old producing another excellent performance to beat higher ranked Czech player Anna Siskova 6-2 6-4.
Klugman, who reached the French Open junior girls' final last year and is currently ranked 341, will now play sixth seed Rebecca Sramkova from Slovakia.
Burrage ensured there would be three British players in action on Friday by beating fourth seed Noma Noha Akugue 6-1 7-6 - winning the second set tie-break 11-9.
She will next play Marina Bassols Ribera, the fifth seed, following the Spanish star's victory over Australian Lizette Cabrera.
There was a big upset elsewhere as top seed Anna Blinkova, the French player currently 72 in the world rankings, fell at the second-round stage as she lost 6-3 6-2 against Suzan Lamens from the Netherlands.
The form of the British trio has helped bolster home fans after reigning champion Mimi Xu, from Swansea, opted not to defend her title this year, instead competing at the W75 Saguenay tournament in Canada.
You can find full results from the Wrexham Open here, external (external site).
Friday, 23 October: Quarter-finals singles & doubles semi-finals
Saturday, 24 October: Semi-finals singles
Sunday, 25 October: Singles final & doubles final