Steve this will be a bit of a wander unfortunately but I have reduced it as much as I can.
The paper I referred to gave a maximum wave height at the lizard, diminishing as it went towards the Severn Estuary. There would seem to be no records of casualties from the Gwent Levels or Somerset Levels from the Lisbon Tsunami, which would comprise the most vulnerable area especially if surging occurred as you suggested. According to Wiki: " Although there is no record of the overall death toll, the 19th century French writer, Arnold Boscowitz, claimed that "great loss of life and property occurred upon the coasts of Cornwall" I do not see that reported anywhere else. Perhaps the surges occurred during the neap tides. I cannot find a way of reconstructing tide tables that far back, sadly.
There are reports that say the waves were seen as far as Galway and the Thames estuary, as well as damage to the south of Portugal and the other side of the Med.
Conversely the meteorological event of On 30 January 1607, around noon, the coasts of Bristol Channel suffered from unexpectedly high floodings that broke the coastal defences in several places. Low-lying places in Devon, Somerset, Gloucestershire, and South Wales were flooded. The devastation was particularly severe on the Welsh side, extending from Laugharne in Carmarthenshire to above Chepstow in Monmouthshire. Cardiff was the most badly affected town, with the foundations of St Mary's Church destroyed.[1]

Floods resulted in the drowning of an estimated 2,000 or more people, with houses and villages swept away, an estimated 200 square miles (51,800 ha) of farmland inundated and livestock destroyed,] wrecking the local economy along the coasts of the Bristol Channel and Severn Estuary.

The coast of Devon and the Somerset Levels as far inland as Glastonbury Tor, 14 miles (23 km) from the coast, were also affected. The sea wall at Burnham-on-Sea gave way, and the water flowed over the low lying levels and moors. Thirty villages in Somerset were affected, including Brean which was "swallowed up" and where seven out of the nine houses were destroyed with 26 of the inhabitants dying. For ten days the Church of All Saints at Kingston Seymour, near Weston-super-Mare, was filled with water to a depth of 5 feet (1.5 m). A chiselled mark remains showing that the maximum height of the water was 7.74 metres above sea level.(courtesy Wiki)

To give this additional perspective:The Severn Estuary is dominated by tidal processes. It has the second highest tides in the world, with an average mean tidal range of 6.5m at neaps and 12.3m on springs. . Tidal range increases further up the estuary, and high spring tides reach as far as Tewkesbury when river flows are low . The Estuary's high tidal range is caused by a combination of factors: an uninterrupted tidal setting for North Atlantic tidal wave propagation, amplification of the wave as it is constrained and converges in the Estuary, and a resonance effect due to its distance from the Atlantic amphidrome . The tidal curve is complicated by geomorphological constrictions and the partial impoundment of the ebb spring tide by the flood spring tide.
Severn bore
Large spring tides commonly lead to the formation of a tidal bore The Severn Estuary is particularly vulnerable to surges because of its orientation and due to its topography and coastal configuration. There is debate over where on the Estuary is most exposed to surges. It may be that the surge level builds as it travels up the estuary and thus threatens the upper reaches more, or that the surge amplitude reduces as water spills out onto the floodplain as it travels, thus affecting the lower reaches more. Thanks to the Severn Estuary's massive tidal range, only extremely large surges or those that occur near high tide have the potential to cause flooding. For example, even a 3m surge would not exceed the mean high water level if it occurred at low or mid tide. The largest recorded surge event on the Severn Estuary was a positive surge of 3.54m, recorded in March 1947 at Avonmouth, but fortunately it occurred at low water on a neap tide,so large scale flooding did not occur .. This was a far larger surge than the 1.45m surge of 1981, which occurred closer to high tide and caused extensive flooding along the north Somerset coast.
Storms
.
The Severn Estuary is particularly vulnerable to Atlantic storms because of its topography and coastal configuration, orientation with respect to prevailing winds, and tidal setting, which together enhance surge heights from storms tracking east and north eastward .

If the event of 1607 was a Tsunami rather than a meteorolgical event several things do not make sense.
The effect was very localised. This surely rules out Tsunami. The reported casualty rate was very high but there are no reports of damage elsewhere, or casualties. This strongly suggests a storm surge.
The Lisbon earthquake created damage on a continental scale(at least)
yet the effects were far more subdued than the event of 1607, that was both localised and of far greater severity.
   My conclusion is that as it stands there are too many assumptions and a woeful inadaquacy of hard data. I would say in conclusion that since the Storegga Slide storm surges have presented the UK with a far greater risk than tsunamis.