I will assume you are currently working full-time (40 hours) 5 days a week?
With that assumption, the difficulty with your plan is in order to comply with the weekly rest rule, is that you’d only be able to work as a HGV driver 1 day per week every other week. So your number of days at work would look like this - 5,6,5,6 etc.(the 6th day being your day as a HGV driver)
This is because of the EU driver’s hours rules, specifically the weekly rest rule. A driver must take an unbroken rest period of 45 hours each week, think of this as your Saturday and Sunday off. However a reduced weekly rest period can be taken of a minimum of 24 hours every other week, so this would be like working Saturday and just having Sunday off.
I imagine most agencies won’t be interested in you if you can only work 1 day every other week. I might be wrong though, you have nothing to lose by making a phone call or a quick visit to an office.
Good luck with training if you choose to pursue it!