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As with anything, it depends, no?
If you have a concrete / other type of impermeable surface up to the side of your house, a French drain will mitigate any damp being held against the foot of the wall (particularly if it was previously above the DPC, or if there was render down to floor level that crossed the DPC), even if it just lets it down to the next impermeable layer (which is, hopefully, much lower than the DPC).
It also has the benefit of reducing splashing back, if you have it filled with gravel / shingle.
French drains are only as good as what they empty into. In London this is often clay or other unsuitable strata.