I increased all of the buffer sizes, max_connections, thread_cache_size - in fact, pretty much every value in the list. max_connections had to be added as it wasn't there already. All the buffer sizes were quite low.
Unfortunately I wasn't clever enough to save the original for comparison....d'uh.
The original my.cnf was the default as per perferct-setup installation - I hadn't made any changes before getting the connection errors.