We are a medium-sized academic research lab whose main outputs are new statistical methods for analyzing large datasets. We generally develop in R and MATLAB/Octave.
I'd go with Python and PyQt4 for the UI, and use Rpy to interface to R.
There's the QtDesigner for interface designing and you can generate python from that. QtAssistant gives you a fully hyperlinked documentation set for Qt which is the best I've ever used.