The lowercase is very close to Bertham (by Frederic W. Goudy, Steve Matteson) but the uppercase is quite different...

The letterforms show the hallmarks of the work of F.W. Goudy, as shown for example in Goudy Old Style http://www.myfonts.com/fonts/bitstream/goudy-old-style/ but I did not spot an exact match to any digital font.
F.W. Goudy is known to have designed over 120 fonts, including ones that were for private purchasers. See the list at http://www.goudyfonts.com/shop-numerical/
Other persons have designed fonts in Goudy's style.
It is possible that this is a private font for Smythson that uses an expanded width of the letters.
BTW you do not provide a reference for your statement "I agree with the author of the below thread who loves the curly in the end of the R."
Don

I saw the the suggestion by Fivo's of Goudy's Bertham for the lower case after I made my post. I also saw that you added a link to the previous thread. I checked the link in that thread to Monotype Classic Roman.
If you use Monotype Classic Roman for the upper case and Bertham for the lowercase, and expand the width you will be fairly close to the font being used by Smythson .
Don

An interesting alternative is to combine Goudy's own Forum
http://www.myfonts.com/fonts/ascender/goudy-forum-pro/ for the upper case with his Bertham.
don

Thank you both for this excellent help!

Upper case Classic Roman + lower case Beltham looks pretty darn close to Smythson's. I should point out that I put the Classic Roman into bold and left Beltham not bold to get the right combination. I've attached an image of how this looks to compare to my photo to see for yourself.

I've

That looks very close. The dots on the i's are about the only obvious mismatch, although the spacing looks a bit too tight in your re-make. You can adjust the tracking to spread it out more.

Do you want me to mark this one as solved with those two fonts?

- Mike Yanega

Yes, you're correct with the spacing, spotted it just after I uploaded, here's a better version.

The lower case k is a little off and some of the capitals and lower case don't quite sit well together (see "Together" and "His") but again some playing with character spacing can probably fix that.

Happy to mark this as solved although maybe "solved" isn't quite the correct term, we know the typeface is a Smythson proprietary one - but we've found a good match.

I agree Paul, that we do not have a match which "solves" the font ID. What we do have is a way of creating a pretty close duplicate of the Smythson font.
Don