Hello
I think for & you can use Garamond:
http://www.whatfontis.com/Original-Garamond-BoldMultilingual.font?text=-
and for JKP you can use Futura Medium:
http://www.whatfontis.com/Futura-Medium-paratype.font?text=JKP
Alex
I found it using: http://www.whatfontis.com - Identify the font you are looking for!

The |J|, |K| and |P| look to be simply Futura. Can’t ID the |&| sorry, it looks familiar but I can nearly never remember the font based purely on the ampersand.

1) As previously said, very generic, nothing really specific. Suggestions by Alex look fine to me.
2) sorry, don't understand what you want exactly... Do you mean "Bond Street"? Because I wasn't able to spot any "Brook Street" lettering anywhere... For the rest, Smythson identity has been designed by Saturday. They may use some bespoke typeface for all their materials. On their website, thery're using Brandon Grotesque and Electra Display but I suppose it's not the one you're after.
For the rest, can't get out of my head that main woodmark SMYTHSON could be easily done starting with some Futura Extra Light manually extending differently each letter. It's some sort Engravers Gothic/Blair/Sackers Gothic extended.
Some more "Futura-like" (letters needing to be stretched: Semplicita, Agenda, Contax Pro, Okojo
Some "Extended Engravers Gothic": Aviano Sans, Montag, Sweet Sans, Luxury Gold, Capline, Zeppelin (41), Doublewide, Adrianna, Biondi Sans, Halogen, Idlewid, Burin Sans, Ronsard Crystal

Thanks to all for the info so far!

I should have made the "Brook Street" identification process easier from the beginning. Please see the images at the following link (I took screenshots from the Smythson site): http://imgur.com/a/lr9X9

Anyone? (Please see the link I posted above with screenshots of "Brook Street" - Smythson)

Smythson appears to have a custom logo and to use a number of proprietary fonts. One of them has an internal name (in pdf's) of "Add-GermainCup". Others include AddLower-BrookW and AddLower-BrookB. One of these is quite close (but not identical to) the logo

Thanks HVB to confirm what I've said. So definitely custom typefaces exclusively for SMYTHSON. So, you could still have a look to my previous suggestions.

Thanks for the feedback.

I was just confused because users kept mentioning the Smythson logo, and I wasn't sure if people were actually analyzing the font in the link to screenshots I posted on Feb 18

Here's a closer look to Brook Street embedded as webfont on Smythson website. Definitely very close to some Engravers Gothic/Blair/Sackers Gothic, for the caps at least. Lowercases is serifed though, the very big difference.

Ryuk: thanks!