As I understand it:
Come next Easter.......(to be confirmed!)
If you want to fly an aircraft on a Certificate of Airworthiness (i.e. a Cessna or Piper) you will need an EASA licence.
This is because CofA aircraft are in Annexe 1 of EASA's regs and from next Easter-ish you will need an EASA licence to fly an EASA aircraft.
Your "Group A" licence is a UK one, not an EASA one.
Of course, an EASA licence also requires an EASA medical!
Your - now revalidated - UK CAA licence allows you to fly EASA Annexe 1 AND EASA Annexe 2 aircraft, until the rules change.
But after then you will be restricted to Bleriot monoplanes, Spitfires, homebuilts and three-axis microlights! (Annexe 2 covers basically those on a Permit to Fly: ie. historic aircraft, warbirds, homebuilts and microlights)
You will, of course, be able to self-certify your medical online for the UK licence but not the EASA one.
One option, which I recommend to all, is to get both a LAPL and your "Annexe 2" licence (which could also be an NPPL SSEA for other readers).
The quirk about the LAPL is that it is for life but the currency requirements have to be met before each flight, rather than on the signing day every two years. So if your LAPL lapses you can use the "Annexe 2" licence on a home-built to re-activate it.
As far as I know, the CAA will now only re-issue "old" PPLs with a Annexe 2 restriction, even though all this is only meant to come in in 2018.
Hence why most GA instructors just say: get an EASA licence.