MkIII inner band is 17.5 mm inside.
Assuming there is a difference in size (placement on the barrel) for a MkIII and a Mk1 band, the later being smaller.
What is the correct inner measurement for a MK1 inner barrel band?
I can't help you with measurement, but yes, because the inner band for a Mk1 is in a different spot to the inner band on a MkIII, they are different sizes.
A couple of things to consider here.... Depending on what you are out to achieve.
The inner band does nothing in a rifle with a correctly fitting foreend. It was added, along with the barrel centering stud inside the nosecap, to minimise the effect of a warping foreend on the rifles accuracy in an attempt to reduce the need for rifles to go back for new foreends if the foreends warped a bit.
The inner band is tapered inside... You can confirm this by sliding it on a barrel one way, Mark how far it goes on, then turn it around and check it the other way.
As a suitable work around, you can use a MkIII inner band on a MkI simply be turning it around... If it is needed to "tame" a warped foreend, it will do the job, otherwise , as I said earlier, it does nothing anyway.
Would you like to expand on your situation, might be able to help with a solution....
I now realize I have a MkI innerband. The PO forced it on the barrel to the MKIII position to fit in the MKIII forestock.
Had to put it in a vise (leather protected) to get it off. I understand these should easily slide into place.