I checked that top hat link. I see they also do bowler hats. I quite fancy having a bowler hat. My local pub insists that I remove my baseball cap when I go in there (video cameras) but I think their attitude would be a bit different if I was sporting a fine bowler with my initials in gold on the hat band.
On the other hand, having bought the bowler I wouldn't be able to afford to go in the pub for about a year. Being a gentleman I would take off the hat indoors anyway, but then I could demand a hat rack. They don't even have a spittoon, so low have their standards sunk.
I would recommend my favourite brand of monocle. The name is engraved around the edge. However when I take it off I can't see well enough to read it.
A stout cane is also worth having for when perambulating in the city. It also affords some protection against unruly blaggards and footpads. I would prefer a swordstick but the constabulary have already warned me about that and it remains at home under the bed.