Many hours later in my development...
@ MF
Of course your analysis of the cause of my syntax errors was spot on. Couldn't see the forest for the trees. I like to think that I'd have quickly spotted the error myself if one of these conditions were true:
1. The squiggly red underline were situated anywhere near the actual cause of the error
2. The column number nn in the (QE-DEF-0260 Parsing error before or near position: nn) pointed anywhere vaguely near the element causing the error
3. There were any correlation between 1. & 2.
Of course, none of these conditions apply, which is just one of the many reasons why we love Cognos, isn't it?

So, according to the original criteria (cf. my first mail), i.e. using a date prompt and checking if it falls between [namespace].[query subject].[S_POLICYCONVERSION_START_DATE] and the corresponding _END_DATE, I got my filter working correctly. So far, so good.
But then, talking with the DBA, we realised that there could be several "versions" within a given day, given the likelihood that at one or more of the five underlying tables would be updated during the day. We decided that a
datetime prompt, rather than just a date prompt, would be needed to retrieve coherent results.
@ dougp
I said that I'd bear in mind your suggestion to carefully check data types & formats. I just didn't know at the time just how important that would turn out to be

So now, I want to compare my prompt input in datetime format against my actual DB fields. No more CAST (S_POLICYCONVERSION_START_DATE, date) etc. So what the DB fields contain is a value which (in my DB mgmt tool 'Aginity') shows up in the format:
2016-05-09 20:42:43
And so far, in several attempts to provide a datetime prompt in a format which correctly compares with the DB format, I've gone from the original:
(#prompt('Business Date : ', 'date','current_date')#
and tried both:
(#prompt('Business Date : ', 'timestamp','current_timestamp')#
and:
(#prompt('Business Date : ', 'datetime','current_time')#
I'm not totally surprised that none of these work. Of course, I could play at combining and reformatting the output of one or more of the above, but time is a bit short, and I'm sure that someone has already had to do exactly this.
So, for those who, understandably, didn't have the patience to read through all the stuff above, here's the executive résumé of my requirement:
1. I have DB fields in format 2016-05-09 20:42:43
2. I want to prompt the user for a value which correctly compares with this format
3. I would like the prompt box to default to current datetime
TIA
Michael