That's a very expensive laptop to be transporting on a bike.
Indeed. I might offer an alternative and light hearted viewpoint on insurance that a younger version of myself might have heeded and wasted significantly less money in the process. I don't mean to speak out of turn, but if you can't afford to cover the loss of your laptop or bike out of pocket in the event of a crash, you're using too much laptop and or bike! Insurance for anything other than a catastrophic loss is clever trick designed to skim wealth from plebeians to the rentier classes. Do you buy the extra warranty from argos for their goods? I'd like to hope not*. If we take the emotion out of it, insurance is purely about managing risk, it only makes sense to buy insurance if you perceive the chance of loss is high and the fees are low. If this is the case, and the loss isn't catastrophic, the alternative to an add-on insurance is to manage your risk by riding safely at all times and being visible in all conditions and avoiding riding in a careless manner that will see you smash up your possessions.
Commercial insurance really only makes financial sense when covering yourself from catastrophic losses, i.e. being sued for crashing into a porsche that carries premium repair costs (we're talking tens of thousands here), or for those things you REALLY cannot afford to replace, like your house that just burnt down... anything else, you need to think really hard about if it's worthwhile. We may well get some anecdotal evidence crop up, some guy is bound to chime in and explain he dropped his expensive laptop/phone/*insert gadget* (that he couldn't afford to buy without monthly payments) in a toilet and thus he was quids in when his insurance company paid up, but he did a bad job of managing his risk and paid for the privilege... Not only did he lose his voluntary excess, he didn't get new for old, he got current valuation of the make and model, lets not forget he had to fork out the initial premium too, all things being told, he'd be lucky if he got 60% of the value of what it would cost to buy an equivalent new laptop, and thus has to cover the difference anyway. If we use your example of the £2400 laptop, we our savvy insured lost £960. This risk could have been managed by buying a fancy pants £100 waterproof case, a fraction of the cost of managing the risk via insurance.
If you really must carry a £2400 laptop, I'd bung it in a shock proof style briefcase and carry it in panniers. Anything short of a car crashing into your panniers will keep said laptop safe, and if it is a car thats dunnit' then, their insurance is going to have to cover it!
*If your answer was yes, please disregard everything above, oh and I have some extra special offers on laptop on insurance to sell you.