Grammar

Other than preference for what I consider flow, I have no firm argument why I'd like this sentence,

'...an elderly lady well wrapped up against London’s chill while inching her mobility-scooter home asked whether I could spare one of my precious roll-ups'.

To read like I intended and not include the commas others are insisting on below,

'...an elderly lady well wrapped up against London’s chill, inching her mobility-scooter home, asked whether I could spare one of my precious roll-ups'.

Too much hesitation in the wrong places, I think. Is there a rule that makes the case for either being correct?

I'd re-write it slightly to:

'...an elderly lady, wrapped up well against London’s chill, asked whether I could spare one of my precious roll-ups when I encountered her (as she was/in the process of etc. if you want to make it clearer who does this) inching her mobility scooter home'.

Minimises commas and flows better, I think. The other version tried to pile too many things on top of one another in the wrong order. Mobility scooter should not have a hyphen.

Generally, if you feel that there's a lack of clarity and you can't get rid of any of the elements, don't hesitate to expand slightly to explain their relation with one another. Also think about splitting it up into shorter sentences if possible--English gives you very little help (compared to, say, German) in constructing complex sentences. Obviously, cutting out elements, if possible, is often the best option. It's often hard to rethink a sentence that you've just written, though.