This is covered by Section 88. Re-applied for licence, so covered until adviced otherwise whilst case is being processed.The DVLA rules are quite clear - even if their letter wasn't - that, given the circumstances stated, he can keep driving while they process the renewal application.
As for insurance, check your policy and check with your insurer if in any doubt.
In this case, though, the DVLA did specify in their letter "Driving must cease" pending medical assessment. Not sure why, but they did.
Even if they hadn't, it is probably safest to report to your insurer any medical condition that you have reported (or should have reported) to the DVLA:
The Association of British Insurers published 'An Insurer's Guide to the Disability Discrimination Act 1995' which says "... it may be lawful for you to refuse to offer cover until the condition is notified to DVLA and you know the outcome of their decision".
... and if Alzheimer's is diagnosed, follow the Alzheimer's Society advice:
A person with a diagnosis of dementia must also immediately inform their car insurance company. If they do not, their policy may become invalid.
Driving and dementia
http://alzheimers.org.uk/site/scripts/documents_info.php?documentID=144
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