Parts of it, yes, and not the parts you would guess from a map of the river. The rivers-and-sea zones barely touch the town. The postcode-level risk indicators tell a much less comfortable story. The difference between those two pictures is rainwater with nowhere to go. This is a town where the flood question is answered street by street, not by looking at Wellington as a whole.
Start with rivers and sea, because that is the measure most buyers have heard of. On the Environment Agency's flood zones, around 2% of the area's postcodes fall in zone 3, the higher-probability band, and under 1% fall in zone 2. Those two are separate bands rather than nested ones: zone 2 is the additional medium-probability fringe sitting outside zone 3, which is why it can be the smaller of the two. On rivers alone, Wellington is largely out of it.
Surface water is where the picture changes. The town grew up around watercourses that once drove its mills, and the ground has been built over steadily since. Nothing in the Environment Agency's zone mapping captures that, because those zones do not model rainwater runoff at all. The postcode-level indicators do, and they are the reason this answer is not a two-line dismissal.
Looking forward, the climate-change allowance pushes the river-and-sea share to around 3% of postcodes. That is the modelled future footprint rather than today's, and it is a modest widening rather than a step change.
For insurance, the practical consequence is that Wellington as a whole is unremarkable and specific addresses are not. Anyone buying here should get an indicative quote on the exact postcode before instructing a solicitor, because a surface-water rating that never shows up on a zone map is precisely the sort of thing that surfaces at the quote stage and changes the sums.
Taking every indicator together, including surface water alongside rivers and sea, around 19% of Wellington's postcodes carry a high rating on at least one measure, around 23% a medium one and around 43% a low one. Those bands overlap with the zone figures rather than adding to them, and the "at least one measure" wording is doing real work: a postcode can land in the high band on surface water alone while sitting nowhere near a flood zone.
Counted as homes rather than postcodes, the Environment Agency's rivers-and-sea mapping puts 498 properties in Wellington at some level of risk. Of those, 168 are high, 39 medium, 49 low and 2 very low, with 120 of the high-risk ones residential. Only postcodes carrying some risk appear in that count at all, so it is a picture of the affected part of town rather than the whole of it.
On whether anything stands in the way, around 2% of postcodes sit inside a modelled high-risk extent with no defence present, and around 2% sit inside one where a defence is present in the model. That second figure is not reassurance. A defence in the model means the model knows a structure is there, not that the structure will hold, not that it is maintained, and not that your particular house is behind it.
Sea level is a background factor rather than a live one here. The nearest tide gauge, at Devonport, recorded a rise of around 2.35 millimetres a year across its 1962 to 2015 record. That is a measured historic rate at a coastal gauge, not a forecast, and Wellington sits inland near the Blackdown Hills.
There is no recorded historic flooding in the area's records. That is genuinely worth something, and it is worth less than it sounds: it means no flood event has been recorded against these postcodes, not that water has never come through a door here.
Flooding is the weakest thing about Wellington, and it is weak in the sneaky way rather than the obvious one. Put the exact address into the Environment Agency's long-term flood risk service, get the insurance quote early, and do not let a clean river-zone result talk you out of asking about the drains.