It can be surprising what can be useful on a CV that most might think is unrelated.
Have you got payslips for yourself for the last 5 years for each month? That proves you weren’t in jail, coupled with a CRB check to confirm can help you get into some agency work.
Big gaps unaccounted for can raise question marks and since you are your only reference, things like payslips can help prove you were doing what you said - If ever questioned
What was the unrelated work ? For example if it was an electrician driving a van, you have a working knowledge of regional and trunk roads, you can plan routes and manage your own time. If I remember rightly you’ve said you have helped a friend move their horsebox around in the past? 
There’s experience of a larger vehicle right there, albeit limited. If the horsebox was old, which is common, it probably had a paper tacho too ?
Depending on the type of work you’re going for, agencies aren’t that bothered about the CV, as long as there’s no gaps as already mentioned, you have a pulse, haven’t murdered anyone recently, have less than 6 points on your licence and there’s a chance you might turn up to the shift they’ve booked you for.