Johanna Konta is playing well atm, into the quarter finals at the Eastbourne champs after beating 2 time Wimbledon champ Kvitova She's not really English either though
Probably not till the next generation of young British/English players come through. Kyle Edmund is the current best ranked English player being British No. 3, behind Murray and Bedene, but I don't think he'll ever be a grand slam winner, he's 21 and from Yarkshire
Best chance of an Englishman or woman winning is if they make it a closed tournament FFS at thread title btw