Brand new car (imported and unregistered but UK spec) or from a dealership, through proper channels for 1300 more?

UK dealership car has 3 years unlimited mileage warranty, imported car has 2 year 60000 miles warranty.

otherwise identical.

What are the pitfalls of an imported car vs one sourced through a dealership?

Skoda Octavia Vrs TDi if it helps.

Go UK main dealer but haggle like hell to reduce the differential. The full main dealer support (with courtesy car etc) for 3 years is worth a lot, and an import will be worth significantly less when you come to sell it

As Capn- Main dealer and haggle like crazy. £1300 is nowhere near enough difference. I'd see the troubles you might see ahead as similar to a Cat C/D right-off.

In the trade.

You will pay for it at trade in time, with a loss greater than that saving. As said haggle for a UK car.

Check the online brokers – UK cars at import prices

Still getting full dealer backup on my '05 plate Octavia, have had the cruise control and air conditioning temp. sensors replaced under warranty this year, ie year 4 and still things going wrong, I get an octavia courtesy car when it goes in and no bills at the end.

The only time I'd buy an imported car would be a European car/order myself and drive it over. Manufacturer is still liable under EU laws I think?
Or a Jap import of course.. 8)