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One thing about driving is that your choice of a workplace is vast and wide ranging, it sounds to me that you would like to work days only, the more constraints you put on your hours of work the less you will earn, if you would be happy working locally for a skip hire company or the council i’m sure you could find hours to suit, supermarkets might be able to cater for you too, but imagine you will be driving a rigid vehicle, not a big articulated truck.
Hi,from the hours you’d like to work I’d say a builders yard is your best bet as they tend to only deliver locally so you’d get a later start.
In general driving wise they tend to want you at your first destination before “traffic o’clock” not leaving the yard just when the roads start to clog up,my Average start time is 4am,sometimes earlier sometimes later.
What days you work depends on the buissness your working within,as said builders yards tend to be mon-fri plus sat morning til 12 and normally you’d work the Saturday every other week.
Personally I think you will struggle to find anything full time with those start times/working days as with every buissness sector now weekends or certainly Saturdays are part of a “working week”.
If you want a home life stay where you are, the only way to make a decent living wage in this game is to put in the hours and lots of them.
If you think you are bored in your present job you’ll be twice as bored HGV driving, waiting around in RDC’s for hours is just one example of many.
You may be bored now, but at least you know what time you’re going home
Make a list of what you want and what you don’t want out of a job. Research jobs advertised and see what is on offer.
There are driving jobs that fit the hours you would like to work and there are some that pay a decent wage. Expect early starts though if you want to be home every day.
3663 is a multi-drop company that pays a decent wage but it involves hard manual work. They advertised for drivers in June up here in Scotland and had over 200 applications for 3 vacancies so not an easy place to get into.
P&H have increased there hourly rate to £10 but you are expected to work rotating Saturdays. Wages are always going to be a discussion point but then again are office workers so well paid?
Without any experience you have very little chance of getting into a well paid , easy job 
(do they exist), so be prepared to take anything you can get in the beginning.
There are companies that take on inexperienced drivers but the pay will show that.