Uniform illumination is a key requirement in different research fields. However, this requirement is often difficult to achieve when high intensity is required at the same time. Recent advancements in LED lamps allow nowadays for compact and economical solutions. In this work we present a suitable solution for various laboratory purposes requiring stable, uniform and high intensity illumination. The system is composed of four identical high power white LED arrays of 30 mm diameter each, placed on a supporting and cooling structure having a minimum volume of 26 cm x 26 cm x 8 cm. A numerical model has been developed, based on a ray tracing software, in order to simulate the performances. These have then been experimentally validated with measurements of the power density map, carried out with a 1% uncertainty pyranometer. Data show that the built system is very stable over time and provides an illumination uniformity higher than 98%, on a surface of 50 mm radius, which reduces to 95% on a surface of 75 mm radius. The power density can be adjusted in the 390-1360 W m-2 range, not affecting uniformity.