Both before a hypothetical invasion and when one actually began, the British assumed that the Soviets would collapse in the face of one, so the answer in short is yes. In this they matched most people in major positions of authority in the rest of the world, Axis and Allies alike, outside of the rare naysayer. The Chief of the Imperial General Staff gave the Soviets seven weeks. His eventual replacement was a bit more optimistic, giving them 3-4 months or so. General Ismay, one of Churchill's chief military advisors, said that the Germans would go through them like a hot knife through butter. I've got estimates ranging from three weeks to ten days as well.

The British did dispatch a military mission to coordinate with the Soviets, but they also had the job of providing Britain with intelligence as to the war situation, helping encourage resistance (especially if the Soviets collapsed; even a guerilla war out of Siberia was seen as useful), and aiding in the destruction of key resources, like Baku's oil fields, if (more presumably when) the Germans were going to capture them. (The head of that mission gave the Soviets three weeks, by the way). Promises of material aid were made almost immediately, but as Churchill later said in his memories, talk was cheap, the sort of support Britain could readily afford; it took a while for it to translate into measurable practice.

Beyond that, the British war effort was in some ways improvisational at this stage, in that while they were secure in Britain, they in turn being on an island (and being heavily outnumbered) meant that they had difficulty translating aggressive ideas into meaningful strategy. Churchill's overriding mantra was aggression, but where and when and how had to be determined as the war unfolded. When news of Barbarossa broke, one of the first British reactions was actually to prepare for a renewed invasion attempt of Britain, because it was thought possible that the Germans could rapidly wrap up their eastern campaign and swing back west; it wasn't until the end of July that they thought that threat had passed. As the campaign dragged on the British felt confident enough to dispatch more armour to North Africa, thinking Britain was safe for at least the year.

Broadly, the initial stages of the campaign, with the outcome up in the air, did almost nothing to change Britain's strategic priorities: defend their Middle East/North African position, encourage rebellion on the Continent, build up a strategic bombing force, and hope that the US would enter the war. Had the Soviets fallen as was assumed, Britain would have carried on. Only when it became clear that the Soviets would probably last did things really begin to change, but at that point the US (and the Japanese) had become involved and it was really then a whole different war.