Helped establish

No. The British had no influence in the interior of Arabia in the mid 18th century when the first Saudi state emerged. British control of India which eventually prompted the British to exercise greater influence in the Persian Gulf was still barely extent at the time. The treaties that began to establish that hegemony in the Gulf were still decades away and never extended to internal politics or to the Arabian interior.

Spread

Again, no. There is a case to be made that the British helped the Al Saud in their conquest of Arabia, but I think it’s a weak one. It would be more accurate to say that the British declined to stop them in some instances, specifically the conquest of the Hejaz, but did in others, including Kuwait and the Saudi raids into Jordan.

Saudi religious doctrine didn’t play into these decisions.

By the time Wahhabism really spreads as part of a dedicated Saudi effort in the 70s and 80s and since then, the British Empire can’t really be said to exist, and the decisions were made by the Saudis themselves.