Whatever any printed lyrics may say, the line, as sung by Alan Bell, the composer, is

"When first we met, complete total strangers".

I have always felt this to be really awkward as well, (although not as awkward as Niamh Parson's adaptation) and whenever I have sung this I have altered the line to

"When first we met, we were total strangers".

This scans much better, IMHO.

Whatever, it is one of the best parting songs I know.

Murray