Unfortunately I don’t know where a table of approved heat pumps is (maybe the BRE website somewhere?). I did this over a phone conversation with my EPC assessor and he was checking a list within his EPC writing software (not sure which one). Sorry not to be more helpful!
Any EPC certification needs to meet BRE requirements, so as you say, BRE is probably the place to look. The table, if any, is, in effect, a scale of recommendations, so it ought to be public but the BRE might have other ideas.
Edit: I have had a look on the BRE website and assume that what we are after is under “Domestic Annual Heat Pump System Efficiency (DAHPSE)” but I haven’t found it yet.
When I couldn’t find the heat pump table we are looking for I asked BRE and this is what they sent:
https://www.ncm-pcdb.org.uk/sap/pcdbsearch.jsp?type=362&pid=31
It isn’t what we wanted but could be useful non the less.