I thought it might be helpful to point out a few things about foreign postings. Obviously, the best way to get them is to get either FCO (which is of course a semi-separate scheme) or DfiD (which isn't but is very popular and only takes a small amount of fast streamers). Plus of course, if you're happy with Brussels as a foreign posting, getting on the European fast stream guarantees you six months out there with the potential for a permanent job if you past the EU's own tests (very difficult according to most people).
Beyond these three, I don't believe that any other department is better or worse for getting a foreign posting. What you need to bear in mind however is that once you're in, there's a Civil Service jobs website which advertises both one year secondments and occasionally, permanent transfers and a good number of these tend to be foreign postings. It's worth pointing out however that we're talking more Afghanistan and South Sudan (both places that people from my own department of DfT have recently got sent, via the FCO and DfiD respectively) than anywhere glamorous. As far as I can tell, there just aren't enough people wanting to do the dangerous postings so they open them out.
There are also sometimes year long policy roles advertised on the same site for those two departments. Once you've got a foot in the door, then whilst you'll have to battle your home department's HR to to not be dragged back at the end of the year, with a bit of networking you ought to be relatively able to stay there and maybe move into a foreign role. Weirdly, the special, better than anything else status that the FCO holds within the fast stream assessment process seems to disappear into thin air and it's no more easy or difficult to get a secondment there than it is anywhere else.
You can also apply to do the same six months in Brussels thing that European Fast Streamers can if you're central departments.
There are also some sort of reciprocal schemes, where, if you've got the language skills, you can spend a few months working at the equivalent department to yours in another country eg. I could go to the Italian transport ministry. I'm not aware of anyone who has done this recently, but I'm planning to look into it for my own interests and if I find anything else out I'll let you know.
Finally, I'm aware of a few people who've managed to get year long secondments working for the UN, in one case in New York, in another out in the field somewhere, but unfortunately can't tell you any more about that.
In summary then, if you don't pass for FCO and aren't lucky enough to get DfiD, don't stress about what other department would be best for foreign postings, and don't decide not to take a job offer. Just take a role wherever you're posted and then keep an eye out for the sort of opportunities discussed above.