How important is securitisation for funding mortgages?

Very. The FT quotes research by Meredith Whitney at Oppenheimer which suggests that since 2000, the volume of US mortgage lending financed by securitisations was seven times higher than the level funded on balance sheet. In 2005-07 alone, securitisations accounted for $2,500B of American mortgages, compared with $431B for on-balance-sheet loans. (I'm paraphrasing rather than quoting as the FT article is so badly written.) And that is one reason why you'd better hope the plain vanilla RMBS market comes back to full health fairly soon.
Update. Deutsche has a nice graphic on the rollercoaster of securitised mortgage lending: