Also sorry to hear about the uneconomical repair. Personally I think you're on goodwill as far as RS goes, it'd be different if the purchase price were £500 though, SOGA would easily apply then.
Bang goes my theory about the disk running file system checks on start up, but as the problem only seems to appear on start up it'd suggest a power supply problem either external or internal on the pcb. Annoyingly I couldn't imagine the disk, pcb or power supply costing more than £30 each and unless there's been a lightning strike I couldn't imagine more than one of those three failing at the same time.
If you get no joy with RS then a local old style tv repair shop might be worth a look, but unlike Humax who with experience of the returns probably already know exactly what the problem is any outside repairer will have to spend time diagnosing first.
Again if there's no joy with RS you might, armed with the box in hand on a quiet weekday morning, ask if they'd be so kind as to try a replacement power supply whilst you wait. It'll either work or not, if it does it points to the power supply, if it doesn't it points to the pcb or drive and the drive can be taken out with care and tested in a caddy/docking-station/pc etc. and you may be able to deduce which major bit is at fault.
Alternatively try it on ebay as non-working or take it to the tip and stack it alongside all the other 'beyond economical repair' and at times 'bored of' electronic goods.
I recall watching a programme about self help repair clubs a while ago, along the lines of this:
https://www.thegoodlifecentre.co.uk/repair-cafe/
brilliant concept.
good luck and let us know how you got on.