Usually, yes, once we understand where the water is actually going. It might be a blocked or collapsed drain, a soakaway that's silted up or was never big enough, ground that's been compacted or built up, or a hard surface laid with falls in the wrong direction. The fix depends entirely on the cause, so we'll come and investigate rather than guess. Our building background helps here — we're used to tracing water problems back to their source rather than treating the symptom.
There's an order of preference set out in the building regulations: a soakaway first, then a watercourse, then a surface water sewer, and only as a last resort a combined sewer. Connecting clean rainwater into the foul sewer isn't permitted on new work — it overloads the system and causes sewage overflows in heavy rain. So the first question on any drainage job is whether your ground will take a soakaway, which needs a percolation test to establish.
It depends on the soil and on space. Clay drains slowly and can make a soakaway impractical, or require a much larger one; a high water table can rule it out entirely. There are also siting rules — a soakaway needs to sit a safe distance from buildings and boundaries, which is a real constraint on a small town garden. A percolation test tells us for certain before anyone starts digging.