It is an early US built Savage as it is a Mk1 rather than the 'wartime expedient' Mk1*
The 12 or 13 prefix was towards then end of the MK1 models as around 120,000 were built and 1,000,000 Mk1* were built
If yours is a 53 prefix and if it is a Mk1 it is a bit of a questionable oddity, throw in the fact it doesn't have the US Lend Lease ownership marks give me some concens as to what it might be.
I am pretty sure that Savage did not restart making Mk1s after building almost 500,000 Mk1*
This is the second Savage I seen recently with the Mk4 rear sight fitted with the MK3 sight leaf. Savage generally used the MK1 sight and later the MK2. The other one turned out to be a 'put-together' bitsa with components from India,
USA
and the
UK
An un-numbered (scrubbed) bolt is certainly a civilian fitted item - it is important that only bolts properly fitted and matched to the rifle are used with that rifle - hence the bolt is numbered to the rifle. It would never have left service with an un-matched bolt.
Can you post pictures of any and all other markings on the metalwork and the woodwork ?