If you're serious about cycling as your main form of transport, you'll need some decent pannier bags to lug stuff around. Above I'm struggling to hold up 30kg plus split into a pair of Ortliebs which I'd just taken of the rear rack of my bike. They're tried and test design and production is the benchmark of pannier bags. Waterproofing to the extent where they can be fully submerged. They'll set you back close to £100 for a pair. Pricey, but worth every penny. I have easily packed the food shop into these, training gear, clothes, if it fits into the bag and not too fragile you can transport it on your bike using these, and in comfort. Having a heavy back pack on while cycling is far from.
Here's a crazy test of their strength.