Nice find. It's a genuine Savage production 4 T converted by H&H. It has travelled a bit, & the scope & bracket, though genuine are not the original issue with this rifle. The E prefix serial on the Rose Brothers bracket indicates in was originally fitted to a 44 BSA. The scope is a Houghton Butcher Mk1. Judging by the serial it is one of the last Mk1's they made, before switching to the Mk2. The cheekpiece I'm afraid, looks like a home made job, & replacing it with a proper one would be one of my first jobs if I owned your rifle......but that may just be me. The scope has been refurbished at some point in its life; those notches cut into the ocular lens retaining ring have been put there by a civvy restorer to ease unscrewing it, although one sees a lot of scopes that show this feature & it doesn't bother me unduly. The forend of your rifle is a replacement, as Savage rifles were almost always stocked up in stained birch, & your forend is beech. However, it may well have been on a long time. If you take off the butt from your rifle you should see the last four digits of the rifle it was factory fitted to on the tenon that fits into the butt socket. If they match with the serial of your rifle it's the original butt.
Is there a scope serial number on the butt under the back of the bolt/cocking piece? Many Savage rifles were left scopeless & so would not have a scope number here.