We made the same mistake when we toured New Zealand a couple of years ago. We thought we would be unlikely to repeat the trip and so we allowed 1 month's motorcaravan hire to 'do' both islands.
Started at Christchurch and found that to keep up the proposed timing we would be spending all our time driving, and that's on roads much easier (less crowded) than the UK.
In the end we only briefly looked at North Island because we spent much more time on South Island. We would love to go back, and probably not bother with North Island because there were still many places in South Island that we only got a tantalizingly brief glimpse of...
The UK is much more crowded and with the itinerary you have proposed you will only see a lot of roads!
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