Kevin: John is correct in that the 'Enfield' action referred to in this case is NOT the SMLE #1 MkIII or the Mk I #4, it is either the P-14 or the P-17 action which was chambered for either the 303 Brit or the 30-06.
With the P-14 action, you can rebarrel to larger, heavier rimmed cartridges as the P-14 bolt was designed for the rimmed 303 Brit. The P-17 bolt was designed for the rimless 30-06.
Gunnut is also correct in that the SMLE actions, and in particular the Mk I #4, the latest version in 303, have been rebarrelled to the 45-70 and the 45-90. Gibbs Firearms produces these rifles and they were advertised in my last Shotgun News. These actions can also be chambered in the 45-90 and both the 45-70 and the 45-90 operate within the same pressure ranges as the 303 Brit.
The major pain with thse conversions, before Gibbs figured it out, was how to make the original double stack magazine feed the cartridges from a single stack conversion and this problem has been written up in articles from the 60s and 70s when this was first tried.
If you want to build a custom rifle in either of the calibers you mentioned, select either a P-14 or a P-17 action depending on your case design. I also saw these actions for sale in my alstest Shotgun News, so they are available. But, if you are going to start a project for a custom rifle, why not consider a Mauser action????? Mikey here to confuse ya.