Tor just ran From Bow Ties to Sneakers: Fashion Tips from the Doctor.
From a gaming perspective, check out Russell Bailey's thoughts on this and other stylistic issues.
Going further back, see the Time Lords in Citadel's 1985 Doctor Who miniatures range, most of whom seem to have escaped from Carnaby Street and/or the Globe Theatre.
So if creating a new Doctor or some other eccentric out-of-time type, even if it's for a regular tabletop game rather than a LARP, take a moment to consider the look.
The silhouette. The coat. An accessory, like a hat or a scarf. A signature prop, be it a new sonic, a fob watch or an umbrella.