Identifying the nature of the dark matter that dominates the mass distribution of galaxies and that plays a key role in our understanding of cosmology is a central unsolved problem of modern physics. Attention over the past 30+ years has focused on weakly interacting dark matter (WIMPs); however, a smaller but active community has been searching instead for 'hidden-sector' particles, including the 'QCD axion', using some of the world's most sensitive electronics. Axions were invoked to solve the so-called strong-CP problem, whereby the theory governing strong interactions is far more symmetric than our current theory, quantum chromodynamics, say it should be. But axions also turn out to be a natural candidate for the mysterious dark matter. Theory suggests that axions should be detectable through the tiny signals they emit, about a millionth of an attowatt, while traversing a microwave cavity in a strong magnetic field. These signals are at the limit of what can be detected using even cryogenically-cooled ultra-low-noise electronics, but in the past few years, rapid progress in developing newer and more sensitive quantum sensors, fueled by parallel research in quantum computing and measurement, has placed the detection of axions within our reach. The UK has considerable expertise in these new quantum devices, and this proposal aims to apply these pivotal new measurement technologies to the search for hidden sector particles. Our proposed search has two main parts. First, we have reached out to the world's most sensitive axion search experiment, ADMX, proposing to form a UK-USA collaboration. ADMX has welcomed this approach, and is keenly encouraging our participation. The UK will design and install a new axion detector inside the magnet and cryostat that ADMX already operate. Using this detector, we will search for axions in our Galaxy's dark matter halo in a previously unexplored mass range between 25 and 40 micro-electron volts. This range is well matched to indications from current theories of what the axion mass might be, although the possible range of masses is far larger, and so there is a great deal of ground to cover. The UK instrument will have at its heart one of our own superconducting quantum measurement technologies - a bolometric detector, a coherent parametric amplifier, a SQUID based amplifier, or a qubit based photon counting device. The technology to be used will be selected after extensive characterisation at participating institutes. The chosen technology will then be integrated into the ADMX instrument module, which will be characterised in a dedicated 10 mK cryostat at the University of Sheffield. This same cryostat will then double as the first target in the UK high-field low-temperature test facility that forms the second part of our proposal. Second, an internationally competitive UK effort in hidden sector physics needs a world class UK facility incorporating an extremely high field magnet: several times larger than those used for MRI imaging in health care. Such a magnet is necessary for axion searches, and axions are arguably the best motivated hidden sector dark matter candidate. The bore of the magnet needs to be very cold for the quantum electronics to work, about 10mK. We will partner with a national laboratory to build and operate a UK facility meeting these specifications. Many hidden sector search experiments could be housed in this facility, but the first one will be our own low-temperature quantum-spectrometer. Finally, to help maintain the UK's international prominence in fundamental physics, we must create a research community. Hidden sector physics is a rapidly growing subject, and the discovery of a whole new class of particles would drive particle physics into a new era, and quantum electronics into new applications and markets. We believe that the technology and techniques developed will have applications in areas as diverse as quantum computing, communications and radar.