Supply difficulties, material and manpower shortages, and Soviet suspicion.

When Barbarossa began, Britain had little hope that the Soviet Union was going to last. They assigned a military mission to Moscow, but their main goals were to gather intelligence for the British and to assist the Soviets in blowing up everything when (not if) the front collapsed and the Germans came charging through.

It took some time for this attitude to change; you can see signs around early August 1941, but even then it wasn't certain (it wouldn't be until considered safe until after Stalingrad). In any case, what British troops were available were tied up on home defense (because the German invasion was going to come any minute now, an opinion held onto well after Barbarossa began), and because after defeats in Norway, France and Greece and the ongoing Desert Campaign, there really wasn't much to go around. But no later than November 1941 the British are looking at sending troops into the Caucasus area (I have records to this effect; conversations on the topic may have started earlier, but certainly not before September, since Iran was not under Anglo-Soviet control at that time). There's no possibility of sending a great field army to the Soviet front, because the British don't have one lying around and the lines of communication from the Middle East through the Caucasus (which is where the British effort would have to come from) were exceedingly poor. British planners said "you can either send Lend-Lease supplies through the area, or support a small force through the area, but not both." The Soviets weren't really interested at that time.

Cut to mid-1942. The Soviets have held on long enough to make Lend-Lease and the development of the Persian Corridor something worth investing resources in (and the British and Soviets have jointly occupied Iran in search of a practically non-existent Nazi fifth column, itself a fascinating story). While the Desert Campaign continued, and the new war in the Far East still further stretched British resources, the fact that the German campaign in the East for 1942 focused on the Soviet south made the British nervous: the Germans were advancing at great speed towards the major source of high-quality British fuel, Abadan in Iran (there were other sources in the area as well, but Iran was the big producer in this period). This drive also increasingly threatened India. So the British considered dispatching forces into Soviet territory to meet the Germans as far forward as possible and again asked about this.

However, logistics in the area were still garbage despite attempts to improve things as rapidly as possible, and British studies soon realized that between available forces (few) and the ability to support them that it wasn't going to be much of an effort. With those considerations, the best contribution the British could make would be to pick a relatively narrow and defensible area, like the Caucasus mountains. So, the British continued to offer to station forces in the Caucasus to hold a line, rather than marching right to the front, with the real goal of being a forward guard of British positions rather than a rear guard of Soviet ones, but Stalin was contemptuous of this idea and turned it down. I would assume, but can't be sure, that Stalin was uncomfortable with the idea of British soldiers in the rear, especially guarding the area of the Baku oilfields; you may recall that the Germans had leaked Anglo-French plans to bomb Baku they found after they captured France, going to great lengths to publicize them to sow dissent. Lastly, for the Soviets, supplies going to the front would obvious be of more use that British troops hanging out in the rear.