The rifle is one manufactured for the commercial market by BSA post WWI (my best guess, civvy rifles are difficult to date).
Andrews was a bespoke London gun maker who probably purchased this one directly from BSA and retailed it through their store. They could have regulated it or might have merely retailed it with their name stamp applied.
The markings underneath the hand guard would tell us a lot. Depending on the rifling in the barrel, it could be generally refered to as a Mk.II* Lee Metford, or most likely, a Lee Enfield Mk.I.
But purists will tell you that only military contract rifles should be referred to by model and mark.
The model being a commercial version did not have to be built to a sealed pattern so could have variations from military specs.
Metford rifling has seven groves, Enfield has five.
The magazine fits and functions is a bit of luck. Usually No.4 series mags are too squared in the body and too tight to fit the long Lee mag well. Methinks that the rifle could have been converted to fit one. The magazine cut off is not original and is the type fitted on the Sht.LE, designed to work with the SMLE magazine which is set up to feed Mk.VII pointed bullet ammo.
The sights are re-calibrated, yes, probably for the Mk.VII ammo, although the ranges seem unusual. The rear sight leaf cap is taller than standard so this all could be part of the regulating by Andrews.
Andrews typically sold these rifles to shooters who wanted them for range use and service rifle competitions. It likely has not been shot a lot unlike its military counterparts.
The scoop out in the wood under the volley is just something to help you get your finger under the arm to lift it. They all had them, but some were shallow and some of them have disappeared because the stock has been sanded to death.
Difficult to say how it came from the retailer as now it shows subsequent modifications by past owners who sporterised it a bit. The barrel looks uncut full length. It was probably to full military specs with a nose cap mounting a bayonet bar
Markings in the metal under the handguard and on the underside of the barrel would tell us a lot more.
Albeit modified, it is still a very good quality rifle.
The extractor claw on the bolt head looks very much like that used on 22 rim fire trainers. What is the caliber of this rifle?