36m in 3km sounds like doable on a 2-speed. However, as much as I love my 2-speed, I just got a 6-speed. The gear changes take some getting used to between 2 to 3 and 4 to 5 and back, but the slightly closer ratios certainly help with acceleration, and give me the granny gears I may need on some climbs (not required yet). I really wish I'd just got the 6 speed to start with. As much as I love the more direct feeling with the 2 speed, the slightly closer ratios on the 6 is better for me, and all round, more practical, although this could be 'new bike' feeling as well.
For most routes through London, the 2-speed is fine, and a good bit lighter than the 3 speed rentals with hub dynamos. But I don't carry my bike much as i love riding it, so that saving seems a little pointless. Moving from an 2016 M2L to a 2018 M6L, I'm not finding it any heavier to be honest.
I don't think you should just buy a bike for a particular small ride. Buy it for what you'll find yourself wanting to do with it once your get your riding legs back. I rented a brompton so that I could bail out of a ride to and from work if it was too much. But once it wasn't, I just got into the fun of riding a brompton to work. e.g always being able to drop guys on road bikes at the lights without even having to get out of the saddle due to less inertia, etc.
If you think you might get to love riding your Brompton, and ride more than that 3km... get the 6-speed.
ps. One thing... rear puncture on a 2-speed is slightly easier than on a 3 or 6 speed ... less pieces to worry about on 2 speed.
pps If you have Kojaks and have 4 punctures in 7 days, and then buy a CO2 inflator, you'll never get another puncture