Sam,
You revived an ancient thread, which also drifted a little.
As GtE gave the details for how to get details on specific aircraft, let me generalise, since I think that might be what you are after.
Two types of airworthiness in UK: Certificate of Airworthiness (CofA) and Permit to Fly (PtF)
ps. There is also some sort of EASA non-expiring things, which everyone seems to think is going to expire sometimes! That's EASA for you! So I will ignore it.
Three types of aircraft: big ones, medium sized ones (ie light aircraft) and little ones (ie microlights) Of course, some microlights have bigger wings than their light aircraft equivalents, but hey, let's keep things simple!
All big ones are on CofA, medium ones can be CofA or PtF, and microlights are all PtF.
All big ones are factory built.
Some medium ones are factory built, and if manufacturer is still around then they are all CofA. If manufacturer is not around, or has surrendered them - like with De Havillands for example - then they may be CofA or PtF. If kit/plans/home built, they will be PtF.
If a little one (ie microlight), they may be factory-built or kit/home/plans built. All are on PtF, and you can only use for "commercial" purposes - ie flight training for cash or hiring - factory-built ones There are, as always, some small print exceptions with this and all the above.
EASA has simplified matters with Annexe 1 and Annexe 2.
If it has a CofA it is in Annexe 1. That means it is too expensive to maintain ;-)
If it is in Annexe 2, it is a warbird, historic, home/plans/kit built, or microlight. It is on a PtF, so maintainance is affordable.
But you can't - at the moment - fly a PtF aircraft IFR or at night.
And then there are balloons (other than EASA), gliders, airships, helicopters, gyros etc.
Other terms, such as light sport etc, are foreign to the UK - often used in the USA.