That BBC chart is focussing on the gross foreign debt of each country’s banks as opposed to the net debt in order to demonstrate the exposure of each country to another in the event of a default. The net debt isn’t so large.
If you want to know the net debt, for example the UK banks you need to click on the UK and add up all the numbers for the countries that owe them. Then click on all the other countries in turn to see what the UK banks owe them.
For the UK, they owe EUR1404Billion (I assume the 1.7 trillion shown in the information box includes outher countries not shown in the diagram) whereas they are owed EUR1566.8Billion so superficially not too bad if no-one defaults.
Ireland on the other hand, as noted above, don’t look good by any measure, their gross debt only seems to be offset by a relatively paltry EUR113.5Billion.