This proposal describes a programme of research on single-particle and collective radiation-beam-plasma interactions at high field intensities, production of high-brightness particle beams with femtosecond to attosecond duration, new sources of coherent and incoherent radiation that are both compact and inexpensive, new methods of accelerating particles which could make them widely available and, by extending their parameter range, stimulate new application areas. An important adjunct to the proposal will be a programme to apply the sources to demonstrate their usefulness and also provide a way to involve industry and other end-users. The project builds on previous experiments and theoretical investigations of the Advanced Laser Plasma High-energy Accelerators towards X-rays (ALPHA-X) project, which has demonstrated controlled acceleration in a laser-plasma wakefield accelerator (LWFA), initial applications of beams from the LWFA and demonstrations of gamma ray production due to resonant betatron motion in the LWFA. The programme will have broad relevance, through developing an understanding of the highly nonlinear and collective physics of radiation-matter interactions, to fields ranging from astrophysics, fusion and nuclear physics, to the interaction of radiation with biological matter. It will also touch on several basic problems in physics, such as radiation reaction in plasma media and the development of coherence in nonlinear coupled systems.