Actually, they didn't keep most building in the UK off prying eyes any more then the germans did of their ship yards. UK shipyards were frequently bombed, and like the germans, they dug out afterwards and just went back to work. One source I have mentions that the shipyards along the Clyde produced 1,526,000 tons of merchant shipping during 1940-1944. Other figures I do have for the Royal Navy
Aircraft carriers in commission 1939 - 7, by 1945 - 58
Destroyers in commission in 1939 - 184, by 1945 - 277
by class, the cruisers saw the largest proportionate losses, from 66 in commission in 1939 to only 35 in 1945 (although some of those represent ships transferred to service with other commonwealth nations).
read more at
http://www.naval-history.net/WW2CampaignRoyalNavy.htm
The allies did have the advantage of foreign shibbuilding. A lot of corvettes and frigates were built in Canada. They also had access to the worlds largest iron ore mines, including the massive one at Bell Island, NewFoundLand.