I'll talk to most people and enjoy an exchange of pleasantries, if the mood and contexts are right. (I'm northern, for what that's worth). I once dialled an incorrect mobile number and got an unknown bloke in Co. Antrim - we chatted for a full 40 minutes and it was wonderful! But being accosted in public I do not like: I find it intrusive, particularly when I'm a lone woman. And yes, it's always men who are the intrusive, persistent ones ones.
I've had a bloke (in London, where else?) ask me to tie his shoes for him. My curt response: 'ask a man'. I've had a guy try to put his hand in my bag on a crowded tube train, shouted at him to take it out, and he was rounded on by a bunch of absolutely wonderful fellow female travellers. I wish I could thank them. I recently willingly chatted with a bloke halfway to London all about the evils of AI. Conversely I've also had abusive responses when I've moved one of my headphones to one side and politely said I wasn't looking for a conversation. Then there was the persistent bloke across the aisle on a flight to Canada, trying to get me to tell him where I was headed once we landed. That one scared me.
The type of guys I have chatted with have not been the types who have been pushy and persistent - which was the reason I was happy to talk to them in the first place. The type of guy who approached OP in this narrative would have immediately been given extremely short shrift.
Many of the responses on this thread are ignoring the very real risk-assessments women have to conduct every day of our lives, or assuming that those of us who legitimately feel we don't owe random men our time and attention have a stick up our backsides. (Or, gods forbid, a job in the City). Random men should learn to leave women alone and take the ample cues they are given when we don't want to interact. Why so many men choose to ignore these obvious hints and persist even when told 'no' is the problem you'd think worth studying on a mostly female support site.
Yet, unfortunately not. For female socialization directly in action, just cast your eyes upthread.