NOT quite.
Same nominal diameter and pitch, but different FORM.
Martini breech threads are the same as a SMLE; i.e. a SPECIAL "Enfield form".
At a pinch, and if you can find a Lithgow "H" barrel lying around somewhere, go for it.
Some "creativity" may be involved to get everything lined up and headspaced.
If money is no object, I hear there are companies in your neck of the woods making NEW .303 barrels of one sort or another.
Another option may be to contact some of the folk who specialise in "butchering" fine old guns for the "deactivated" market and see if you and your local dealer / gunsmith can do a swap for an undeactictivated barrel of the correct or approximately correct pattern.
Biggest caveat: All the other usual "warnings" regarding reviving "downgraded" arms apply.