My partner and I are relocating to London for...

My partner and I are relocating to London for work (around Westminster and the City). We are adult students on a gap year and will both be working in London on fixed-term, full-time contracts, earning £25,000 per year each, with additional parental financial support available if required. We are currently based in Paris and are non-smokers, with no pets and no adverse credit history.
We are looking for an entire one-bedroom flat, ideally furnished or part-furnished, with a budget of around £2,000 pcm (utilities and council tax not necessarily included), and a late February move-in. Our intended stay is around six months, with flexibility if required. Our preferred areas are Central London in Zone 1 or very well-connected Zone 2, to allow an easy commute to Westminster and the City.