Did your girlfriend finish her degree in the last 12 months - if so she can probably qualify for a Tier 1 (Post-study work) visa which will let her stay and wor

Did your girlfriend finish her degree in the last 12 months - if so she can probably qualify for a Tier 1 (Post-study work) visa which will let her stay and work in the UK for up to two years (at which point she'd be expected to switch to a different visa if she wants to stay). But the important point is that it wouldn't be contingent on her having a job offer.