I know what my father would say. He'd say if you're going to lose the friend over it, you may as well not lose the money as well. So if you're going to let the friendship cool, why bother paying her more than what is fair? It is messy though if she is also your housemate.
I see two other issues here meself.
The first is that I would never expect someone who was doing me a favour to be liable to the same extent I would expect from a company. A company has a duty-of-care and would also be specifically insured for carriage of goods whereas you aren't. (And while we're on it, would Royal Mail pay £600 unless you used an expensive insured service?) It would be kind for you to offer, but I would only accept your offer to pay if I were borassic and even then moving swiftly on to point 2 -
The second is that £600 sounds like the insurance value i.e. I've lost a bag of clothes and what would it cost me to replace them if I needed them today, not what would it actually cost me to buy a few secondhand (because that's their value if they've been worn even once) clothes over the course of a few weeks on ebay or charity shops.
Realistically, if it didn't contain items that need urgent replacement e.g. her only smart work-trousers, then a few clothes and a handbag is something most people have spares for, and if you're her friend she should be saying 'oh dear, it's kind of you to offer but don't worry about it'. Obviously if my house burns down tomorrow then I'll be claiming on my insurance for every item I had in it because that's what I pay my premiums for, but if I weren't insured (or if the insurance didn't insist I spend the money to replace everything) there are things I wouldn't bother replacing even if I could afford to. Would she even use all the £600 to replace everything you lost or would she essentially be in-pocket here?
Thought experiment: if you had lent her a bag of clothes etc and she had lost it, would you expect her to replace them all or pay for them at new-for-old values? Because if not, then I can't see that you would be being fair on yourself if you pay the £600 she is asking for.