Is an EU single currency still a trade advantage in 2019? When the single currency was planned, there was no internet and there all currency exchange was manual. 

Today the web can automatically convert prices using multiplication of the numbers in the price field, and robotic cash exchange can count and exchange currencies better and cheaper than a human exchange. 

Does the UK suffer an considerable economic handicap from having not adopted the Euro? Is the single currency concept nearly obsolete?
Very good points about the role of modern tools (the web, robotic cash exchange, etc.) are raised. The  classic argument is that trade should expand within the eurozone following (1) increase in price transparency, (2) elimination of currency conversion costs, and (3) elimination of exchange rate fluctuations.   

Are the classical arguments challenged by modern tools?


Price comparison across border is surely much easier today with the web than it was in the nineties.
In  its  report  One  Market  One  Money,  the  European  Commission  (1990)  calculates  that  eliminating  costs  of  conversion  of  currencies  and  costs  of  cover  for  exchange  risk  will reduce costs by .25 to .5 of 1 percent of total output in the EU. The report also stresses additional  gains  that  would  come  from  the  elimination  of  “in-house  costs”  associated  with multiple  units  of  account.  These  are  reductions  in  costs  connected  with  record  keeping,  accounting and decision-making. The question: How much lower are the conversion costs thanks to modern tools? Even if they are now lower, they are still positive.
Despite modern tools, exchange rates still fluctuate.


So, the adoption of the single currency may still boost trade. 

The role of modern arguments

To these classical arguments, we can add more subtle ones. For instance, in some industries, components cross borders many times before being assembled and sold as a final  good,  even  a  small  reduction  in  transaction  costs  can  increase  trade  flows non-linearly (Flam and Nordstrom, 2006). 

In a series of papers, Richard Baldwin adds that adopting a single currency may (1) reduce collusion among competitors and eliminate pricing mark-ups and enhance trade (p. 63-64); (2) increase the entry of small firms by reducing the fixed cost of trade.