Same same but different, as people say in Thailand.
To the innocent eye Bromptons look pretty identical since the invention of the Mk2 in 1987, but there has been a coninuous stream of small incremental changes each year (and sometimes more often) that sum up over time. And obviously some bikes have been modified and retrofitted. Regarding your bike: It has 2018 model brakes and a stem from a MK2 before 2000 and a right hand pedal and saddle with pentaclip after 2008, 3rd party brake levers and shifters from a model after 2005 and possibly a later, mate M bar as well as a relative new mudflap on the front-wheel and probably newer blades as well, also the seat post clamp got exchanged for the newer version from mid 2007 on - though the main frame may be a 2001 - so it is a little bastardized.
"started life off" is obviously true. Can't tell from the pics if the main frame really is a 2001, you would have to refer to the frame number to be safe. What I can safely say is that the main frame dates from before 2004. The Mk2 stem makes me a little suspicious that it may be a Mk2 by birth (Mk3 got invented in 2000 and the OPs bike clearly is a Mk3, completely original apart from the saddle and the thingy on the bars. The shifter looks a little bit like Sram, but this would not fit 2000 and is impossible to tell from the pic).
Regarding the shifting there was a break point between 2000 and 2002: In summer 2000 S/A went bankrupt, leaving Brompton with limited stock of hubs and no supplier. Stocks lasted until spring 2001 and just in time before running out of hubs Brompton managed to squeeze in the SRAM 3-speed hub into the rear frame replacing the S/A 3AW that was no longer available. Too bad that the Sachs/Sram 5-speed hub did not fit, so there was no replacement for the top notch model T5 that was using the S/A sprinter. That led to the development of the half-step 6-speed on the basis of the SRAM hub which was then invented in spring 2002 as L and T6. A tad earlier Brompton fitted the rear frames out with the nut that is necessary for the shifting mechanism - I guess towards the end of 2001. Your bike, being a (possibly late) 2001 possibly has it (or the rear frame got replaced at some point in time) or not whereas a 2000 model doesn't have it. Your's also may possibly have an S/A hub with an aluminium hubshell instead of the S/A 3AW with the steel hub shell or the Sachs hub (hard to safely detect from the pics, I may be wrong here) that replaced the 3-speed Sachs in 2005, so maybe a little bit more of bastardization. The 6-speed used the Sachs until early 2009 when it got replaced by the BWR.
As you can see: Changes over changes and tiny things like the nut sometimes make huge differences.