Unipart started as a brand within the Rover Group parts operation, using the large dealer network as distribution. At the time, other factors might deliver twice a week, wheras the Rover dealer was usually out daily to all areas. Part quality was initially excellent, as they had access to all the OE manufacturers. As competition began to catch up, they had to cut costs, and that is where it all started to go wrong. Buying cheap, and selling expensive, did not win favour with customers. Later they found a middle ground, with good quality, and reasonable pricing. Sadly, the company was heavy in middle management, bringing huge cost, slow response to changing markets, and a long heavy process to introducing new parts. (Initially I worked in the warranty department, later in the parts intro process.) At least, while slowly sinking into the abyss, it bought me a house, although, like the parts, is not high quality.
Unipart bought a factor chain, Edmunds Walker. They had a chain of outlets countrywide, with a head office staff of about 30. Instead of learning, Unipart insisted on doing it their way, expanding the head office count to over a hundred, and wondered where the profits went. They later did the same thing with Brown Bros/Partco, having learnt nothing, and slid that into nothing too. The Partco guys were all good, but unable to battle against the bureaucracy. Partco and QH were closely linked.
QH started out with medium quality products, and were popular in the trade as being 'adequate', and a good choice for owners with little money, and low milages. Their clutches however, were usually regarded as a last resort, as they were often plagued with judder and early failures. QH saw the light, and upped their quality, taking over their clutch supplier, and changing it to make good quality parts, later used as OE replacements. They did similar with water pumps, moving from 'medium life adequate', to high quality, often better than OE. The Rover A-series engine was known for water pump leaks, the QH replacement used a better seal and lasted significantly longer.
Into the new century, it all went downhill, for both QH and Unipart. Unipart aftermarket is now just a brand, no connection, apart from a licence fee, to the parent company. No idea of their sources or quality, as the sell off happened after I left.
QH disappeared, the name bought by First Line. First Line were initially adequate, then improved, and my last dealings with them was with a company striving to bring good products to market at acceptable prices. Current QH stuff is the same, just with different branding.
Prior to the early 2000s, I was confident with most Unipart products, except their brake friction products. Most was sourced from a supplier with no other aftermarket presence, and my own experience was at times frightening. We used to test fit many of their products, running various vehicles. For commuting around town, their brakes were acceptable, only because you'd probably never use them in anger. In heavy use, there was a tendency for them to fade, worryingly. They improved, but by then I'd long since refused to use them on my own vehicles. Shortly before I left, they were moving away from that company, and going to Mintex, always a good choice. No idea what the new organisaton are sourcing though.
In summary, for the original question, the shocks will be fine, as will the brake discs. The brake pads may be OK, but you wouldn't find me using them, unless their origin could be determined. If they're clearly Mintex, they're good.