Was the ATCO drunk? Seriously, that what it sounds like.
What's the relevance of continually repeating the radio failure procedure? Ironic, since they are in only patchy effective 2-way communication the entire time as it is?!
Think the BA crew come out of this very well....
Brings up a question: Realise the complexity of doing so, but could the BA crew have requested another controller, e.g. a supervisor to be brought on frequency?
PS. Reminds of times in France when have called up a regional airport for zone entry/joining instructions to find myself blasted with a full ATIS at barely comprehensible hyper-speed.