Group A is the old name for what is now called "SEP", and the Americans call "SEL". Basically it's single-piston light aeroplanes.
"Permit", is the category of airworthiness, and can include microlights, homebuilt light aircraft, vintage aeroplanes, jets, etc. It's a totally separate issue to the class.
"Microlight" is a complicated definition based upon weight and stall speed. But being simplistic, look at the permit or CofA document - if it doesn't say microlight on it, it's not. (There's one twin flying in this country which is a microlight, and several light aircraft with 2 seats and an MTOW under 450kg which aren't so paperwork is the best way - you can look it up on the G-INFO website too.)
And yes, you can keep your Group A / SEP / SEL license current on any permit aircraft (including PFA homebuilts) to which that license applies - that is single engine, and not a microlight. You can even do your bi-annual flight with an instructor within the PFA's coaching scheme.
G
N.B. Correcting Beagle, not all microlights are G-M***, and a few flying machines that aren't microlights are G-M***. Times change !