If your engineering group already uses C# then it might not be such a difficult sell - the two languages are highly interoperable, so you may be able to carve out a particular greenfield project and write it in F# instead of C#. Note, though, that we've found it necessary on project `FooBar` to create specific `FooBar.CSharp` wrapper libraries that C# users can consume; this is because idiomatic API design looks pretty different between F# and C#.
(If you're interested in quant finance in London, I work at G-Research which uses F#; I write almost solely in F# there. You can contact me privately if you like at [email protected].)
I saw in a different HN post a few weeks ago that jet.com heavily used F# but obviously that's no more.
If a company were using F# and I were looking to switch and all the other stuff was a good match, the language choice would be a big pull for me.
While I use and am learning F# for a side project, there's no substitute for working with one professionally and shipping production code with it. I wish it'd be possible to convince my engineering group to use it.