Definitely looks like a cut No. 4,which just means you have a cheaper, actually accurate No. 5 pretty much.

This will probably help.

That may not kick as hard.

The marking on the barrel. looks like a navy arms when it was in Ridgefield NJ

In the 1960/s Navy ARms of Ridgefield New Jersey in the US imported large numbers of used surplus Lee Enfields,and had them customised/sporterised into various styles with mismatched serial numbers,as provided the head spacing was within limits,it was a question of putting a gun together with used parts from many backgrounds.
The finish on some of these parts guns was redone,and
they were selling very well.
They still turn up on the U.S. market but are valued
below the original they tried to copy,not only by being
a more common model,but also due to mismatched serial
numbers.

http://www.gunvaluesboard.com/jungle-carbine-lithgow-5078319.html

Yes, it's a cut-down early BSA No. 4 Mk. I.

Note - this rifle has had its serial number defaced (though who knows who did it and when).

The rifle's serial number does not appear to be visible any longer on the wrist. The 1942 is the date of manufacture, not the serial; that would have been beneath it. Can you discern any other numbers below the 1942?

Good deal. Refinishing sometimes made the serial numbers illegible; not uncommon with Enfields. Makes it difficult to identify if the rifle is matching or not. I've got a Mk. III with a nice London Proof House mark over top of the serial on the receiver; it's legible, but only barely.

Yours appears to have the early Mk.1 milled, micrometer rear sight for the No.4; those are pretty desirable anymore.

I went to buy one for my No.4 Mk.1 years ago, turned out to be an actual Jungle Carbine rear sight. Still click-adjustable but different values per click and only goes to 800yd (like I can even shoot well enough to get a hit at 800, never mind 1200! )