Not sure I follow exactly why he would have cared much where he was in relation to England, but generally speaking they didn't have a very exact idea where they were. Latitude was easy enough to calculate, so settlers initially expected similar latitudes in the Americas and Europe to be environmental similar. This of course didn't work out so well for English or French settlers who found North American winters to be much harsher and found it difficult to grow things like grapes in Canada which had otherwise thrived in the same latitude in France.

Longitude, which you also need to figure a more precise position, took much longer to figure out. Early attempts to figure longitude involved making precise astrological observations, this is part of why Cook was out in the Pacific so long, mapping the transit of Venus in multiple locations across the world was important for figuring longitude. However, all that work post dates Colombus by several centuries.

So they could figure more or less where they were in terms of N/S but had to figure E/W by virtue of their speed, dead reckoning, or astronomical calculations. There is a reason why maps from the time period of Colombus often have only a passing resemblance to our own.