To summarise crudely: the tariffs are punitive, to give all producers within the EEA as much of an advantage as the trade negotiators could deliver. And because the EEA represents a wealthy group of around half a billion consumers (very many of whom are not individually wealthy; but collectively are wealthy), the EU has huge negotiating power on trade agreements: probably about even with China and the USA, and superior to everyone else. So countries outside the EEA tend to get a poor deal in general.
There is a wide range of tariffs set for goods and services for countries accredited to the WTO in their own right (the UK is not) - as you can see from your linked site. But each of the EEA's significant trading partners seeks a bilateral deal with it, because the pain is too high otherwise.
That site - the one you quite reasonably describe as "unbelievably complicated" - is as transparent and as clear a description of tariffs as I've seen anywhere. And yet it still has vastly over-simplified matters: there's a host of regulation that goes with the tariffs, to ensure that what's imported into the European Economic Area (EEA) is safe and fit for purpose.
Within individual trade publications, there was some discussion on levels of tariffs imposed on countries outside the EEA for that particular trade: so, for example, the Financial Times had quite a lot of coverage on the potentially devastating effect on the financial sector that provides so much of the UK's income; and various manufacturing industries talked about the existential threat that Brexit poses to them; but as you can see from your linked site, general-purpose publications didn't have a chance of getting into the detail across all goods and services.
