The patents cited by that paper
show no evidence of construction and testing.
But a laboratory-scale model was tested in 2015, says this paper
(paywalled except for the first page).
The J.S.R. paper's set of test firings was even covered by The Economist.
The propellant was half a meter long and burned for a few minutes, with a chamber pressure of about 500 kPa, just a few per cent of the chamber pressure of SpaceX's Raptor engine.
Because these tests ended "due to fuel starvation or, sometimes, another failure mechanism," one might say that this state of the art is still at the Jebediah Kerman stage.
In a 2020 Oct 5
the Glaswegians announced that they will attempt liquid fuel in 2021.
The Defence & Security Accelerator (DASA), part of the Ministry of Defence, has pledged £90,000 for further development of the autophage engine, which is being built at the University of Glasgow’s James Watt School of Engineering.
Autophage engines have already been test-fired by the Glasgow team using all-solid propellant. The new funding will underwrite the research required to use a more energetic hybrid propellant: a solid tube of fuel containing a liquid oxidiser. The engine will be test-fired at Kingston University in London’s new rocket laboratory in London next year.