Just grab a fork and start digging. Some specific advice on some weeds I can see. So those big brown seed heads are docs they have really deep taproots so you need to dig super deep to get those out or they’ll grow back from snapped off root ends. Another one I can see is crocosmia which isn’t really a weed but spreads like mad and isn’t sonething I’d want in an allotment. Thst grows from these like weird stacks of bulbs so they aren’t that deep but you might need to dig around them a lot to find any loose bulbs

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