At the moment, you are not eligible for a UK eVisa:

Who can set up access to an eVisa

You can set up access to your eVisa now if you have a:

• BRP
• Frontier Worker permit

Check if you can access an eVisa if you have another physical immigration document.

The link leads to another page that says in part:

To access your eVisa now, you ... need to have a certain type of immigration document.

If you do not, you’ll need to set up your eVisa later on.

And, near the bottom of the same page:

You’ll need to apply for a BRP before you can access an eVisa if you have indefinite leave to remain or enter and:

• [three inapplicable items omitted]
• you do not have or were never given an immigration document

The link for the

At the moment, you are not eligible for a UK eVisa:

Who can set up access to an eVisa

You can set up access to your eVisa now if you have a:

• BRP
• Frontier Worker permit

Check if you can access an eVisa if you have another physical immigration document.

The link leads to another page that says in part:

To access your eVisa now, you ... need to have a certain type of immigration document.

If you do not, you’ll need to set up your eVisa later on.

And, near the bottom of the same page:

You’ll need to apply for a BRP before you can access an eVisa if you have indefinite leave to remain or enter and:

• [three inapplicable items omitted]
• you do not have or were never given an immigration document

But if you follow the link to apply for a BRP, you'll see that you can't really do that: they've "stopped replacing BRPs."

As far as I can tell, though I haven't found an explicit statement of this on the government site, the eVisa is just the name for the newly expanded program of dispensing with physical documents that was first implemented for EUSS beneficiaries. They haven't yet started using the term "eVisa" for EUSS beneficiaries, and perhaps they have separate systems that are yet to be merged, but both the EUSS and the eVisa give access to a "share code," so the eVisa system works in essentially the same manner as the EUSS: your rights and privileges are established by a database lookup after you present your passport or identity card rather than by the presentation of a document issued by the UK.

You'll probably want to keep an eye on this, because there's a good chance that it will change in some way or another -- there have been problems with the online verification system, and those will only get worse as it is extended to the rest of the immigrant population, so the conditions and procedures may change as the government tries to deal with these problems.