The Chief Pilot of each company you were with can sign your logbook on behalf of the captains. If you've spent all your time with one company then this should be easy. It's his/her job to make sure that your entries are correct (read realistic). Bearing in mind that flight records are not retained for ever this would be difficult to check as time goes by. Just don't go to the CAA aged 23 claiming 5,000 hours on jets. They might notice.