Posted: Today at 13:37
The roots of this thing go metres deep and are brittle so break easily and each bit can become a plant.
Digging over once, and thoroughly, will certainly help you remove major weed roots but, if you plan to be chemical free, the best course of action is simply to keep pulling it up or hoeing it off as you see it. Do not compost it as it will propagate in the heap but you can make a fertiliser from it by soaking in a covered bucket of water for a few weeks and then diluting the resulting pongy liquid to feed plants.
In future, you should be able to do it without digging as it's better for soil structure and the friendly micro-organisms. In autumn, cover bare spoil with sheets of cardboard or even thick layers of newspaper and hold this down with layers of well rotted manure and compost. Where you have permanent plants such as fruiting shrubs, mulch generously. The worms will work all this into the soil over winter and you will end up with a good texture for working, weeding and planting and happy plants feeding on fertile soil and able to get their roots down for moisture.
Raspberries come in two group - early and late fruiting. The former fruits on new stems produced the previous year and it sounds like you have those. Remove all the old, fruited stems at the base and then tie in the new ones to supports. Remove any excess or unruly plants. The late fruiting varieties can be cut back hard to about 9" in spring and will then grow new stems which fruit later in summer and early autumn.
The RHS offers this advice - https://www.rhs.org.uk/advice/grow-your-own/fruit/raspberries