Pretty significant. As : Probably millions of lifes significant.

But answering it precisely is a frickle thing. We need to ask ourself "How would WWII hava panned out if Alan Turing did not contribute in any way". And answering this is...puh. It is basically alternate history, and this is stricly speaking not scientific. Of course it's highly interesting, but giving a definitive answer is probably impossible, especially if we're talking about such a big topic. Good for us : A lot of pretty clever historians and contemporary witnesses have discussed this topic so we can have an idea.

I do need to widen your question though as to make an attempt of answering somewhat possible : I won't look at Turing personally, but at the "Ultra" program, or even more broadly : What would have happend when the Allied were not able to break into Enigma. Let's say the Germans used 8 rotors (like in the Engima H), it would probably have meant the end of the Allied efforts of breaking the code.

Most historians agree that the main reason Germany lost the second World War is because the Allied were able to produce larger amounts of war machinery, man and fuel them. This is the lack of supplies that crippled the Wehrmacht. The second main reason is the lack of proper military intelligence, reconnaissance etc. Since counter-intelligence falls into this big topic it's what we're going to be looking at.

You have to see that in WWII the Allied were able to read more or less every piece of communication inside the German armed forces for most of the time. This is unique in the history of warfare. It is no wonder that everybody agrees that if Enigma would not have been broken, the war would have been different.

Sir Harry Hinsley, who worked at Ultra, famously said that Ultra "shortened the war by not less than two years and probably by four years". Harold Deutsch, member of the OSS (the predecessor of the CIA) even said that Germany might have won the war if it wasn't for Ultra.

The most significant role Ultra played is maybe the Battle for England. In the autumn of 1940 the Royal Air Force was riding it's reserves. Lucky they knew the plans of the Luftwaffe, and the convoys from the US could get through to bring supplies more often than noit, because the locations of German submarines were known. If this would not have been the case, then maybe (maybe) the Battle for England would have been lost. Maybe Germany would have been able to land in Great Britain, and maybe even succeed in conquering it. This would most likely have meant the end of the war. With more forces freed up to fight in the Soviet Union, and probably an earlier start (Spring of 1942 instead of Summer 1941) it is very likely that Russia would have fallen as well. But we can not know that for sure. We don't even know how the US would have reacted if Germany managed to invade Britain. It's all a big IF.

tl;dr : We don't know. It is very likely however that the war was significantly shorter because of Ultra. It is even not out of the realm of possibilities that the outcome of WWII would have been entirely different.

A very good book I can recommend on the topic :

Frederick William Winterbotham: The Ultra Secret – The Inside Story of Operation Ultra, Bletchley Park and Enigma

There is also a book by Robert Cowley which talks about what would have happend if Ultra (and lots of other things in history) didn't happen, called "What if". I did not like that one as much, but it might be worth looking into if you are interested in this kind of stuff