Will the UK lose its right to issue ISINs?

With multiple exchange operators from overseas courting London Stock Exchange Group (LSEG), and with the "Brexit" referendum coming in June, a topical question is - who will issue ISINs for the UK in the future?  One reason for the question is that the UK itself has no right today to issue ISINs.

LSEG has the sole right to issue ISINs for UK financial instruments across all asset classes.  That operation is expected by ISO to be a not-for-profit cost-recovery operation.  Why would a suitor of LSEG want to retain an operational function that isn't a regulatory requirement and makes no money?   Economies of scale are a key justification for exchange mergers and acquisitions, and as the suitors for LSEG don't and can't issue ISINs themselves, issuing UK ISINs brings no economies of scale for them.

There's often a period of "asset stripping" post-merger, where activities that are considered by an acquirer to be "non-core" are sold off or closed down.  Who could take over ISIN issuance for the UK? 

The most obvious organisation is WM Datenservice, which is already the issuer of all ISINs for Germany, and is the "Substitute Numbering Agency" for the UK (and most of Europe and Asia/Pac).  Deutsche Boerse Group can't and doesn't issue ISINs, so if it wanted to hive off the LSEG operation that issues UK ISINs, WM Datenservice might be an obvious new home.  US exchange operators can't and don't issue ISINs either, so if one of them wins the bidding for LSEG, an obvious new home for UK ISIN issuance might be the US issuer of ISINs - CUSIP Service Bureau.

A reason for asking questions like this is that nobody in the UK - not the FCA or the Bank of England or HM Government - has any say in who issues ISINs for the UK.  Should we care about that?