Fuel isn’t the Holy Grail any longer, the old contracts have all but vanished) and judging by the actual pay slip we’ve seen posted here on this very forum and from postings of people doing the job the shift pattern and hours involved, the wages should be nudging £50k not bloody £38k or whatever it works out at.
My advice is probably similar in some ways to what you have been doing already, ie and now for something completely different 
, not hire and reward (unless in a very specialist sector where long learned skills can’t be replaced just like that) cos H&R is just about on its arse, try to find own account work if possible where the job is not haulage but more of a customer service role.
Nothing at all wrong with supermarket work when its direct employed by said supermarket, and seeing as its 364 day work, more likely to find varying shift patterns.
RDC work is fine when you work for the RDC, it’s when delivering to RDCs as a supply haulier which is some of the most demoralising work out there.
Note, as always the best jobs are never advertised and people already there tend to keep schtum about where they work, so get that thinking cap on see whats about and go knock on doors, but the chances of you slipping into an ideal shift straight away are remote, you may well have to (as i did) take whatever is going at first if the job is right in order to get your feet under the table, but if you are competent courteous and take a pride in your work, you won’t be on a dog end shift for long.