I changed my car insurance over (from my old car to my current one) by phone, so I spoke to a 'real person' rather than a computerised system. When asked for the value of my X-reg 1.6 litre Ford Escort (with air-con, alloy wheels and lots of other extras provided 'as standard') I stated "£350" because that's what I paid for it. (I was working for a Ford main dealer and staff were allowed to buy any 'trade in' at £50 more than the company gave for it). I was fully aware that the 'forecourt price' for my car was around four times what I'd paid for it, so I wasn't surprised when the insurance guy questioned my figure. However I explained the circumstances to him and he was happy to enter it into his system.
So, if you simply want the lowest insurance quote, I'd suggest that you should state "£1600". (Based upon my own experience, I can't see how the insurer could claim that you could be guilty of 'fraud by false representation'). Of course, if you're seeking 'fully comp' insurance, the downside is that you'll only get £1600 (less your insurance excess) back if the car is written off in an accident.
Chris