I thought this was an interesting point. If her friend had said no and she had had to leave it in a theatre cloakroom their policies (at least the few I looked at) say something along the lines of:
"please note that the venue is not responsible for any loss or damage of personal belongings".
It seems to me, as I said previously that she is just taking advantage of the fact she's dealing with a person, not a company. Any company which offers to hold your things for free will have a disclaimer that those items are still your responsibility, left with them AT YOUR OWN RISK and the situation should be exactly the same with her friend.
She didn't receive any payment for taking the bag and I bet her flatmate would say the reason she asked her was that the cloakrooms have this policy and she didn't want to risk leaving her valuables. She is just taking advantage and trying to pass all of that risk onto an unpaid friend.
She also sounds like she's too much of a princess to want to have to lug her own case across London as it might have spoiled her designer look.
If she insists her friend is liable for the entire amount, a) I believe she is wrong and b) her friend should work out how much she needs to deduct for the carriage fee and stress caused to her by this situation. Her flatmate is just using her as she did when she asked her to take it.
Personally I don't think that's what a friend does and if she won't come to a better compromise I would walk away, move out if you can because she sounds like she is and will continue to be quite a toxic force in the OP's life.
The OP hasn't said "it's your problem" but the flatmate is telling her 'friend' that it's her problem to find what (to her at least) is a huge amount of money she doesn't have. She is acting as judge and jury over who owes what and manipulating and using her friend's guilt.
If she is so adamant the friend owes her for the entire thing let her take it to a lawyer and see what they say.