Earlier quoted context omitted.
Not even just films. The BBC was notorious for taping over old programmes to save money on tape and thus there's early episodes of Doctor Who that are lost along with some classics such as episodes of Hancock's Half Hour. I'd suggest that tapes should be digitised and that way they're far easier for the public to watch and categorise them so that other hidden gems can be found again.
Are you willing to pay for it? I've been involved in getting the archives of a small-time newspaper digitized and it's not cheap in terms of either time or money. There's a near-infinite amount of decaying and fairly rare analog media out there--and much that has been lost as companies have gone out of business, etc. It's not realistic to digitize all of it.
I'd be happy for some of my tax money to go to a historical preservation project.
Maybe it'd be feasible to get members of the public to volunteer to do some of the digitisation - that should reduce costs, but I can imagine it would be difficult to keep track of where all the originals are and quality of the digitisation.