Sure, you could duplicate the records and work on them - but these are likely to be old COBOL systems working on fixed-width records where the location of everything is hardcoded and the application is covered in global variables. If you're going to refactor one of these applications, you might as well spend the money migrating away from it (into a language the agency can actually hire for).

A possibly more doable approach would be to provide a read-only dump into an external SQL database at the end of every batch job for external systems which desire such a thing, but I'm not convinced there's a whole lot of benefit compared to the cost of doing so. There's no part of the agency which needs the information out of office hours, and it's honestly quite reasonable to say "come back tomorrow" in the few cases where the public might want the information out of office hours - note that the web interface is replacing having to call up the DVLA or visit one of their offices, which would have the same restriction.

It'd be much more reasonable to spend money and the time of the people who have experience with the system attempting to migrate off it. Hopefully they're trying.