Bike Insurance

Right so I need to get home contents insurance for my new flat. M&S is great value until I add a bike at over £4000, when the premium jumps £450 a year. So it would seem much better if the bike which is worth £4000 on the nose.......this could be done by having a lower value groupset and wheels (which I would then claim for if it was stolen). Would this just be a case of getting an LBS to value it lower than its current value in case it was stolen? Or is this fraudulent?
If you tell them it's worth £4000 then you'll only get that amount should it get stolen, rather than the full value of the bike (over £4k). So as long as you are ok with this risk then I *think *it's ok.

It might work out cheaper to insure the bike separately?