After line training in one of the northern UK bases I was sent away to a major Italian base for a mere ten months and now I'm back in a UK base again on a permanent basis. It is indeed luck. Right place right time etc.
I doubt applying for a new base through crewdock will get you anywhere quickly. We had a base meeting one day, I spoke to the guys on the day and a week later I was offered my first preference base via phone call.
An EXTREMELY UNFAIR system but that's the way FR operate. There are base transfers and they do happen. I'm not alone, there was a wave of F/O's from my old base getting their first preference.