You can't do it on line if you don't have a passport.
Other than the Post Office doing it for you, you can do it by post, it's a few £'s cheaper.

You still have to visit the Post Office to get a form though.
From the Gov.UK web site............
Applying by post
Fill in form D1 ‘Application for a driving licence’. You can get it from most Post Offices. Include:
a new passport type photo taken within the last month (do not sign the back of the photo)
the photocard and paper counterpart of your current licence (if you’ve lost either, tick the relevant box on the D1 form)
a cheque or postal order for £17, payable to DVLA (there’s no fee if you’re over 70 or have a medical short period licence)
Send your application and fee (if needed) to DVLA.
DVLA
Swansea
SA99 1DH