I've just seen on Twitter, first person anecdote but I've not seen corroboration, where someone was contacted by Serco Test and Trace and after having been told they had to travel 350 miles for a test they were told that due to lack of lab capacity in the UK, swabs were being sent to Italy for analysis.
I don't doubt it. EUROFINS, one of the contractors are reported in the Telegraph today to be sending samples to their lab in Germany.
Another report in the same paper has said that there were, yesterday, no available tests anywhere in the UK.