Car Category D write off, can I keep driving until repair

Hi all, insurance question I cant get a straight answer on - would love advice please. My car was crashed into 3 weeks ago, bad dent in passenger door, no injuries, no other damage. Other party admitted liability and we took to assessor for quote to repair. Assessor deemed the car a Cat D write off ( its 15yrs old) but told us it was safe to drive out of his garage and on a 6hr roundtrip we needed to take the following day..we continued driving it since.

We want to keep car on tbe road so our own mechanic will fix it in 3 weeks time when he can fit us in. We will get cheque from other drivers insurance of the pre accident value minus scrappage value and pay for repairs ourselves. Have been told we need to get an independent assessor to check the repair is up to scratch which is fair enough. However we are still driving the car now and will be for next 3 weeks - is our insurance still valid ? Yes I did phone my own insurance to query it - twice - dealt with 2 different donkeys who didn't seem clear on what the answer was - one told me I was covered but that I should drive extra carefully until repair is done !

Also who do I present the independent assessors report to after repair - my own insurance company or the company that paid out the write off ? My own company said it was for the other company- doesnt make any sense to me ?!