MK1/2?

The rifle in question was made at the Maltby plant in 1944 originally. 

Might be a AY prefix in the serial number. 

If you are buying the rifle as a shooter, you will want to check bore condition and fit of the forend (wood stock that runs from the back of receiver to the muzzle).  Since it is a Mk 1/3, it’s likely to have a FAZ replacement five groove barrel.  Quite often, these barrels are in good condition, as the Mk 1/2 and 1/3 rifles did not typically see a lot of service use.   It’s best to have a set of pin gages available, these are not expensive, in the range of .302 to .305 (in .0005 increments).  Ideally, you want a bore that is .3025  to .3035.  Larger bores can still shoot well in some rifles.   If nothing else is available, use a .308 bullet as see how far it enters the muzzle.  Muzzle crown wear is common from improper use of the pull thru.

Remove the bolt and look down the barrel from the breech end to see if the rifling still exists just forward of the chamber.  You want sharp edges on the lands.   

Make sure the bolt and receiver serial numbers match, this is important as the bolts are individually fitted to the receiver.  If they don’t match, there is a good chance the headspace may be incorrect and the two locking lugs do not give equal bearing on the receiver lug recess surfaces; in this case, don’t fire the rifle until the bolt is checked for lug contact and headspace is checked.  

The forend should not slide front to back on the rifle.  If it does, it can be repaired but that does take a bit of skill, less skill if you want to repair it with epoxy bedding compound.

Don’t let this put you off of the Lee Enfield.  It is an interesting well designed rifle that can be very accurate for a WWII era service rifle.  Gossic has got his No. 4 Enfields shooting sub-MOA ten shot groups consistently.  

".. I have an M1A so have 7.62 Nato I can use to check the bore,  also have 30-06.

the forend did have a noticeable looseness but I can't remember if it was front to back or side to side..." 

but others smarter than i will respond 

You've got the details from the other's here regarding the rifle.

But I noticed a couple of minor points in your second photo. Firstly, the magazine that is on the table; is that from this rifle? I ask because it is actually from an older no1MkIII type Enfield (WWI type).

Secondly, It appears that the upper hand guard metal is very close to the front sight protector. It has maybe slipped forward a bit. There should be a gap; if it's touching the sight protector it will have an effect on the accuracy.

The .303 British bullet is actually .311" diameter. The .303 measurement is the diameter across the lands of the rifling not the across the depth of the grooves.

Welcome to the Forum.