Let's say that for domestic reasons, in June 1942, just after the fall of Tobruk, President Roosevelt tells Churchill that it's now absolutely out of the question that the Americans participate in any landings in French North Africa that year.
And let's assume that Churchill decides that for political reasons, if the Americans aren't along with it and leading it, the British Empire can't do it, in case it causes Vichy to throw-in with the Axis.
Would there have been any operations that the British and their (imperial) allies could have carried out either on their own or working with the Russians in the remainder of 1942 with forces in the UK that would have otherwise been used in Operation Torch? Would an attempt to liberate the Channel Islands or an effort in Norway have had any chance of success? Or would there have been something else that forces based in the UK could have tried, given potential limitations to distance coverable by shipping and/or air-cover?
If operation torch was called off, the allys would put more effort into the
dieppe raid. No question about it. The british and canadians wanted to make a stand somewhere, and this was where it would happen. They needed to gain experience in naval landings, test the atlantic wall, and see whether or not they could take and hold a port city. If the raid had been better planned, and gotten REAL fire support, then it may actually have been a success.
Historically, there were four flanking attacks made to support the main landing at dieppe. Two of those (orange and green beach) were completely successful, and the other two (blue and yellow beach) had been partially successful. [1] What doomed the entire operation was the complete failure at the main landing site, on white and red beach. The planners mistakenly assumed that if the flanking attacks were successful (or at least not unsuccessful), then the main attack was certain to successful as well. Amphibious operations are difficult affairs by nature, but launching an attack against a fortified port is beyond difficult.
Its like walking into the jaws of defeat and trying to snatch victory. The lack of naval gunfire at dieppe was crippling: Unsupported infantry, no matter how brave, cannot succeed against an entrenched enemy on high ground. If there had been a couple of cruisers to bombard white and red beach, many more soldiers would have been able to cross the sea wall and enter dieppe than IRL. If the engineers had been able to get up to the sea wall, and demolish the obstacles blocking the streets into the city, the tanks would have actually been able to enter dieppe and support the infantry. [2] The inclusion of paratroops (which was cancelled) to land behind german lines would also help.
Things would have went even better if the canadians weren't forced to adhere to an unrealistic and flawed exploitation plan, which included surrounding and capturing the entire city (!), before sending the tanks to link up with the soldiers at green beach... And then penetrating 10 km inland to over run a german HQ... And then landing the royal marines into the harbor to seize the german landing barges, and sail them back to england, before they mounted a major counterattack. Yeah. Whoever thought up this part was a moron.

Check out the map and see how difficult such a foray would be.
Anyway, the point is that a better planned, better executed raid
could have been successful. They would have achieved most of their major objectives, which included seizing a radar station, capturing an enigma machine, and demolishing the port facilitys. Giving the germans a bloody nose at dieppe would have been a moral victory for britain, and would keep the soviets from complaining about the lack of action in the west. It wouldn't have as much impact as operation torch, but it would be
something.
[1] But even with those isolated victorys, there were still problems. The overall plan for dieppe was too rigid and inflexible: The flank attacks had to be completed before the main landings took place. If they were completed after the main landings, their impact would be negligible.
[2] As it was, the engineers were stuck with their open topped scout cars (which they never wanted), and were picked off by the germans before they could cross the beach.