While the Spanish and (to a lesser extent) the French spent much of the 16th Century exploring the New World, the English did not begin doing so in earnest until the 17th Century. If you look at what was going on in England during the 1500s, it is easy to see why their priorities lay elsewhere.
The 1500s were a tumultuous time in England. While the nation was still recovering from the War of the Roses, the Protestant Reformation led to further turmoil in England. This struggle consumed much of the attention of the English monarchs, namely Henry VIII and his daughters, who were trying to consolidate their own power before they could even seriously think about expanding it abroad.
It was also dangerous at this time for England to think about directly competing with Spain. Today, we often think of England as the ruler of the seas. This was not always the case. During much of the 16th Century, that honor belonged to Spain, thanks to its well funded and massive navy. It was not until after the defeat of the Spanish Armada in 1588 that English ships could sail to the Americas without too much fear of encountering the Spanish.