It would be possible to run a low bureaucracy REF that only measures research outputs.
Research England and its counterparts could put all the research outputs in the UK into a big ranking using a mixture of bibliometric and altmetric data (things like total tweets about research) then assign funding based on which universities the research came from.
If this was deemed too narrow even for the most pure outcome driven research fans it would be possible to quite easily add in some data on impact. This could be data on funding, collaborations, total doctoral students, and so on.
A purely metric driven exercise would be significantly cheaper to the tune of several hundred million pounds. And, while Research England would correctly argue the administration of REF represents a fraction of total research spending, it is money that could be spent on actual research, not the administration of research. Although some research would suggest there is low salience between peer-review results and metric results, this could as easily be a criticism of peer-review as it is the cold face of metric driven performance review.