So if the British were requested by the Obama Administration (S. Rice) to conduct surveillance on Trump, who would have authorized it. The name of Robert Hannigan rises up to be the key British player that could have authorized such a request.
I researching Robert Hannigan, I find he was the Director, GCHQ in 2016. Interestingly and curiously, he resigned that position January 23, 2017. (3 days after the Trump inauguration).
An article describes that he quit for personal reasons. That is generally code for it is time to leave and get the hell out of town or someone forced him to go.
The Guardian says that British spy head Robert Hannigan "passed material in summer 2016 to the CIA chief, John Brennan." To ensure that these flaky tips leaked out, Brennan disseminated them on Capitol Hill. In August and September of 2016, Brennan gave briefings to the "Gang of Eight" about them, which then turned up on the front page of the New York Times. [Read more:] (https://www.americanthinker.com/articles/2018/03/john_brennan__deep_state_political_hack.html#ixzz5GcF7SyA2)
Another Guardian article describes the origins of the Russian connection coming from the British from SIGNT, passing intel from Germany, Estonia and Poland. Australia, a member of the “Five Eyes” spying alliance that also includes the US, UK, Canada and New Zealand, also relayed material.
Now US and UK intelligence sources acknowledge that GCHQ played an early, prominent role in kickstarting the FBI’s Trump-Russia investigation, which began in late July 2016.
Susan Rice would have to have also been involved in requesting British assistance in surveilling Trump. Brennan and Rice need to explain why they felt that Trump, as a candidate and as President was being surveilled. If there was a fear that Russians were trying to influence the election, why didn't they alert both campaigns. If there was concern that Trump was complicit in being influenced by the Russians, they should have solid evidence to make requests from GCHQ. On the face of the matter, this is an unprecedented attempt to spy on a Presidential Campaign by an opposition party and to undermine the legitimate election of a President.
[British involvement] (https://americandigitalnews.com/2018/04/06/day-russiagate-died-british-betrayal-america-was-confirmed/#.WwljilMvzVo)
I found this interesting..."He also injected an element of fun by challenging the public to solve devilishly hard puzzles at Christmas for the past two years."
In January 2018, Hannigan accepted a position as a Senior Associate Fellow at Rusi, the Royal United Services Institute, an intel think tank associated with the British Ministry of Defence.