The CofA is issued on the basis of a combination of inspection and a Type Certificate (TC). The conditions of the TC are listed in the TCDS - Type Certificate Data Sheet.
The TCDS lists flying limitations, max and min weight, relevant documentation (POH, Maintenance Schedule, etc.) and in most cases the master minimum equipment list (MMEL). Individual operators may set their own MEL, but it mustn't contain less than is in the MMEL.
For some reason UK CAA doesn't like publishing its TCDS in the public domain - I've had rows with them over that before now. However under ICAO procedures they'll almost certainly reflect the content of the TCDS issued by the country of origin - in this case the US and therefore the FAA issued TCDS. FAA TCDS are online
here and for the PA28,
here (longish.pdf file)
On page 35 it says (I quote)
The basic required equipment as prescribed in the applicable airworthiness regulation (see certification basis) must be installed in the aircraft for certification.
Cross-checking to page 34, it lists (with a stack of caveats and issue states) the certification basis as FAR-23.
FAR-23 you can download from the FAA's website, but I happen to have a copy. It lists the minimum instrumentation that has to be fitted. At paragraph 23.1303 it says...
Sec. 23.1303 Flight and navigation instruments.
The following are the minimum required flight and navigation instruments:
(a) An airspeed indicator.
(b) An altimeter.
(c) A direction indicator (nonstabilized magnetic compass).
(d) <plus lots of other stuff applying to heavy and turbine powered aeroplanes that aren't relevant to this discussion>
So in a nutshell, a compass is mandatory equipment for flying a PA28 on a CofA.
Okay, I'll admit that isn't all that intuitive but the information is there.
G
(or being simplistic, look at section 6.9 of the PA28 operators manual. It lists all the equipment that must be installed (and by implication serviceable). It starts obviously enough with the engine, prop, fuel pump etc. On page 6-25 it lists the compass, Tacho and engine cluster as mandatory, and altimeter and ASI as mandatory unless replaced by an approved alternative.)