Should I let insurer collect my low-value bike? Worried about storage fees

Hi all, quick insurance question.

Last week my bike got reversed into—front end hit. The other driver admitted fault at first (I’ve got the texts), but after I sent my repair quote, he changed his story and is now accusing me of hitting him from behind.

My bike’s only worth about £1,500 and the repair is minor (just a few hundred quid). The insurer’s handler (4th Dimension) wanted me to take a hire bike (I said no, which seemed to annoy them) and now wants to collect my bike, but their storage fees are mad—could easily end up costing more than the bike if there’s any delay.

Has anyone managed to keep their bike at home for assessment? Is it reasonable to push for that? Would love to hear if anyone’s done this or has advice!

Thanks!