Which station seems to carry more local stories from the UK, Mike?
I am probably being thick here. I am not sure whether you mean regional stories, in which case that would be local radio stations in the UK, some of which are BBC stations. But if you mean 'local' as in UK stories, then Radio 4, which is the national station for the UK would have a mix of UK and international stories. They don't really have a local bias as such....if there is war or an earthquake somewhere abroad, that will get preference to whatever is going on in the UK.
I don't know the availability of the BBC abroad via its radio station. You can try listening live via the web from the site I linked you to. But I think the iPlayer with past programmes only operates in the UK.
The World Service is much more about what is happening in the area where the broadcasts are being directed. Some see it as propaganda. I suspect there will be broadcasts to Iran in the appropriate language and the BBC would claim that what they broadcast is neutral and is to inform the locals of the truth. For many in the past this service, and there is an equivalent USA service, may be the only remotely impartial news the population may receive.
Additionally, due to the Commonwealth links, a lot of the broadcasting is also directed to the interests of the member countries.
A lot of the news output I hear ignores the UK.
Mike