I reckon that logging the replacement engine with DVLA should be quite straightforward. Details here.
https://www.gov.uk/change-vehicle-de...idence-to-give
Looks like you'll need written confirmation from a garage. Probably best use one that is also registered as an MOT test station.
Your best course of action is almost certainly to register the change correctly with your insurance company and DVLA rather than to ignore the change.
If the press is to be believed DVLA is a bit chaotic at the moment because their staff continue to "work from home". Best take a copy of your current log book before surrendering it into the abyss.