"...buy a few bolt bodies..." Doesn't work that way with an Enfield. Although it can, but you're looking at a lot of trial and error with pricey parts. A stripped bolt(just the body, no head, firing pin, etc) for a No. 4 is worth $26.50 each at Gunparts.
Headspace on either model is adjusted by changing the bolt head and re-checking the headspace with proper guages. The No.1 and No. 4 use totally different bolt heads.
"...recently bought a 303 enfield...a lower cost alternative..." Yep. However, like MikeG says, which model? Where is the rear sight? On the barrel makes it a No. 1. On the receiver makes it a No. 4.
SAAMI spec headspace guages will be just fine. Brownell's sells them if you want to do it yourself($25 each I think). It's not difficult. Slip the guage under the extractor(or take it out) and close the bolt. It should close on a Go, but not close on a No-Go. Although if it does, try a Field. If it closes on a Field the headspace is excessive. Not closing on a Field indicates the headspace is on the high end, but the rifle is safe to shoot. It's entirely possible your smithy doesn't have a Field. Not likely, but possible.
Fixing the headspace on a No. 1 requires a handful of pricey bolt heads($11.30 each from Gunparts) and some trial and error with the guages until you find one that works.
Fixing the headspace on a No. 4 is slightly easier, depending on what number is on the bolt head. If it's a '0', you try a Number 1, then a Number 2 if the Number 1 didn't fix it. Gunparts has Number 1's and 2's(same price). If it's a Number 2, you have a hunt ahead of you for a Number 3.
I know of a guy, up here, who may have one. Surf over to
http://www.canadiangunnutz.com/forum/ and into the 'Milsurp' forum and ask about them. It won't be $11.30 though. Marstar lists them for a No.4 at $19 Cdn, but doesn't say what numbers they have.
http://www.marstar.ca/le4mk1s.htm