Hi Stokell, I live in the centre of the the country at the foot of the Pennines on the Yorkshire side. The prevailing wind blows East to West 90% of the time off the North Sea. But I would think it would blow in the opposite direction off the Atlantic too!
In anycase, you always want something to look forward to at the end of a trek, therefore you want to be cycling West to East with the East coast to look forward to. The scenery, countryside and the coastline of Whitby, Scarborough and Bridlington and the N Yorks moors are beautiful places and Liverpool pales into significance by comparison.