Which "ATC" was supposed to know that Elstree was not available? ATC could not "direct him to Battersea". ATC cannot order the diversion of an aircraft; that is wholly the pilot's responsibility.
Given the short flight time between Redhill and Elstree I'm surprised neither he or the operator hadn't just called them up and just asked the question "whats the weather like where you are".
Given he lifted at 0735hrs out of Redhill, crashed at 0800hrs in London having found he couldn't get into Elstree -did the weather fundementally change in the time?