When Does a Country's External Debt Become a Problem?
The position is both worse and better than you describe

If you look at Section 7 and Figure 6 of  https://www.ons.gov.uk/economy/nationalaccounts/balanceofpayments/bulletins/balanceofpayments/quarter1jantomar2018 you will find that UK liabilities (public and private) abroad were estimated to be £10,894.5 billion at the end of March 2018, about 5.30 times UK GDP in the 12 months to March

But at the same time UK assets abroad were estimated to be £10,632.2 billion, about 5.18 times UK GDP 

So the net position here was a liability of £262.3 billion, about 0.13 times UK GDP (a minor rounding issue here), i.e. 13% of annual GDP.  In fact the net position is the difference between two enormous numbers largely resulting from financial activity in the City of London, both of which are estimated with errors, so large revisions to the estimated net position is common  

A small UK net international liability represents the position for many years and so in that sense empirically seems to have been sustainable.  For Greece this net figure became large and unsustainable, contributing to its crisis, and not helped by the Eurozone restricting the possible solutions.  The answer to your question "When Does a Country's External Debt Become a Problem?" seems to be "when people start to worry that they will not be able to get their money back and so stop lending more money".  Turkey may be facing this issue at the moment.  But I doubt there is a fixed figure you can identify