The insurer wants to repair rather than replace my laptop, is that allowed?

Generally, yes, if the policy permits it. Many contents policies give the insurer the option to repair, replace, reinstate or pay the cash value of an item. If your policy is a new-for-old replacement policy, the insurer should replace like with like, meaning an item of equivalent type, quality and specifications, and it should not be inferior. Check the wording to see if the insurer is allowed to supply refurbished items or must supply new items. If it is not clear, ambiguity in the wording is interpreted against the insurer. Ask the insurer to explain in writing why refurbished replacement is appropriate, and negotiate a cash settlement that would allow you to buy a new one. If you are not satisfied, use the complaints and dispute resolution process.