You can also get circuit breakers with integrated GFCIs (which is what we call RCBOs); those are usually double-width devices in the US (For example, with the Siemens "QF" product range [1]), however, again, single-width versions are available (For example, with the Square D "QO" product range [2]).
Because a GFCI needs to measure current flowing in both directions, it has an inherent need for a neutral connection too. This is what the flying lead is for. The circuit neutral would be terminated into the GFCI instead of the panel neutral bar; the flying lead is terminated into the panel neutral instead.
I'm also not assuming a ground; a neutral-bonded lamp body sitting on a conductive surface which is in contact with the mass of the earth would still be enough to immediately trip a GFCI under the same circumstances as my previous post, regardless of whether someone is touching it or not, and if it is turned on or not (assuming the switch is in the line conductor).
EDIT: However, this all goes to crap if the lamp only has a 2-prong plug, yes.
I agree that some aspects of US electrical installations are exceedingly bad compared to over here. For example, it is stupidly easy to shock yourself removing a live socket from a wall over there, compared to it being a basic impossibility over here -- yes, I know, safe isolation and all that, but name me a sparky that hasn't done this at least once.
[1] https://cdn11.bigcommerce.com/s-b8b6a/images/stencil/1280x12... [2] https://cdn11.bigcommerce.com/s-b8b6a/images/stencil/1280x12...
Thanks to Big Clive, I have a vague but reasonable sense of what UK electrical systems are like. It's not safe, metaphorically or literally, to assume the US is up to the same standard. As you might find out the hard way if you did make such an assumption, North American electrical systems in a lot of ways are shockingly poor.