The groundwater is one of the most important natural resources. It provides drinking water and water for businesses. The level of groundwater varies in time. It has significantly seasonal oscillations and long-term variations, induced by rainfalls and climatic droughts. The seasonal, interannual and decadal cycles of groundwater level are studied by reconstructed time series for several groundwater stations in England for the period 1891-2015 provided by the British Geological Survey. The monthly groundwater level time series are created by the program AquiMod by real measurements of groundwater level data, precipitation, temperature and estimation of potential evapotranspiration, soil drainage, unsaturated-zone flow and groundwater flow. The common cycles of Total Solar Irradiance (TSI), precipitation and Palmer Drought Severity Index (PDSI) are determined by means of the Method of Partial Fourier Approximation. The solar and climate cycles are compared with the groundwater oscillations in narrow frequency bands with periodicities between 1 and 125 years. The variations of seasonal amplitudes are analyzed together with solar and climate Indices. The possibility of forecast of groundwater variations on the base of common solar, climate and groundwater cycles is discussed.