Yes.
West Bromwich Albion
Wolverhampton Wanderers
West Ham United
Woolwich Arsenal
Watford
Wimbledon
Wigan Athletic
Every single edition of the top division of English football has featured at least one of these.
Wolverhampton Wanderers and West Ham United are currently the only two teams in the English top division beginning with W and they are both in the relegation zone.
Watford and Wrexham (who have never been in the top division) have a shout of promotion.