I would say it's more of a small donkey than an elephant. I didn't have a chance to watch the documentary unfortunately, so I'll reserve my judgement until I find a time to do so.
So you don't know what you're talking about, but you think its only a small donkey, not an elephant. Great. As if the size of the animal makes a difference - its the fact that its stinking out the room, shittting on the carpet, destroying the social fabric of our society, spreading hatred and supremacism, and leading at one end of the continuum to terrorism and innocent children, women and men dying.
As far as I am aware, Saudi funded projects would promote their brand of 'wahabism' which, as you rightly pointed out, is puritanical. However, the caliphate/political element of Islam is usually ignored by the wahabis in this country. This is a source of constant emnity and mistrust between wahabis/salafis and various caliphate groups.
Join the dots - wherever Saudi money goes - extremists of all brands and stripes follow. The East London mosque was funded by Saudis. They gave it its logistical and organisational prominence. Jamaat-e-Islami and other 'Khalifa' types congregate together, regardless of these trifling 'ideological' differences. In the here and now, there are synergies and overlaps between them.
Look at it this way, to use another image. Many different species of flies are attracted to the same piece of dog crap.