If i borrow a car and the tyre needs replacing who is responsible for replacing it?

My wife recently borrowed a friends car to get to work while our car was in for repair. At the time of borrowing her friends car one of the tyres became flat due to a punchure. My wife's first thoughts were to pull over replace the flat tyre with the spare and take the car to the garage for a replacement to be fitted.

When my wife went to replace the tyre with the spare her realised the space tyre wasn't present. She phoned her friend that had lent her the car to tell her what had happened.

Her friend responded by saying she was aware that she didn't had a spare tyre and that she was meant to have sorted that out ages ago. she asked my wife to leave the car where is was and she would get her husband to come and collect it with her.

My wife felt obligated to pay for the replacement of the tyre as she was in charge of the vehicle when the punchure happened, regardless of whether the car poorly maintained or not. To which her friend refused the offer. My wife then came back with a further offer of "Well at least let me pay haft the bill for you then?" to which again her friend refused the offer.

Her friend then up held her end of agreement by collect the car and having the tyre placed. My wife borrowed the car on the 11/1/14 and the tyre was replaced on the 13/1/14.

On the 18/02/14 following a disagreement between my wife and her friend on an unrelated issue to this. Her friend wrote her a letter as followed.

Please see the attached receipt Copy for the cost of a new tyre that required replacing when you asked to borrow my car on the 11/1/14 I will also be sending you another bill on my loss of earnings when I had to cancel calls on the 13/1/14 so I could go and get my car from Nuneaton where you left it.

I believe this to be unfair when agreement was made on the day by both parties having given consideration and acceptance to and given that that this agreement was then re-addressed 39 days later cannot be binding in the terms of offer and acceptance?

What I am seeking advice on is whether or not my wife is liable to pay for 1) the replacement of the tyre 2) whether my wife would be liable to pay for her friends loss of earnings.

I would like to respond to the letter (if needed) as soon as possible. I just want to understand legally where we sit and how best to respond?

PLEASE HELP!!!

Lee