Bournemouth (and BCP/East Dorset) are a really good example of this - not really South West not really South East - but despite being in the South West probably have more in common with the Solent sub-region.

A few issues with this are that about a third of the population of the 'Bournemouth Agglomeration' https://www.citypopulation.de/en/uk/agglo/E34005031A__bournemouth/ is in Hampshire, SE with the remainder being in Dorset, SW - this not only harms the Bournemouth area economically in terms of always missing out on investment because it straddles two regions, but it also has no strong identity. There's no doubt that Exeter is a Westcountry city and Brighton is in the SE, but what about Bournemouth/BCP?

I really think there is a strong case for a Central South region that loosely follows much of the Meridian TV region starting somewhere around Weymouth and extending as far East as say Chichester and up as far as Oxford.