As noted by everyone here, certainly could do the ride on that CB.
Planning on buying NEW? For sure buying in the UK? (cheaper in other countries)What is Total "on the road" cost?

To me, suitability depends on several things: 1. route choices? 2. how much OFF ROAD intended? 3. your riding skill off road? 4. how much you really end up packing onto the bike.

5. I also question long range COMFORT of that bike. Do not forget to add in cost for better seat (not crap foam pad) probably handlebar risers and better bars. Also, add $$ for upgraded suspension, luggage racks ... more.

The low hanging exhaust may be a problem once bike fully loaded. Hitting pot holes, dips or other Whoop De Doo type obstacles may have you bottoming out HARD with stock suspension once loaded, despite your low body weight.

I would give that bike a PASS!

Alternatives?
1. I'd much prefer DRZ400 (E or S model) that has already been SET UP for travel. They are around if you look and are patient. Proven bike, if bought used and fixed up some, could be ideal? (More around in USA than UK, much cheaper too)

2. If planning to avoid serious off road ... consider keeping your BMW. It's fine for most any dirt road and is paid for, sits in your shed now. If you go "Mountain Goat", then not so good.

3. The Falcon is basically an XR400R. If you start your trip in S. America, you could find a good Falcon used. Also, many XR400's for sale in USA (kick start only), some road legal, most NOT.

4. If you're cool with a 250 I would go Honda CRF250L. A better travel bike in many ways over that CB. Proven good travel bike, more money (I'd guess) than CB ... but worth it, IMHO.