My wife hired a car from Hertz which broke down and caused

My wife hired a car from Hertz which broke down and caused her serious inconvenience and distress and we would like to know what level, if anything, we can claim.
The following complaint was sent on 18th June to Hertz:
Thanks to the condition of the car I had the misfortune to rent from you and the lackadaisical attitude of most of your staff, what was supposed to be a pleasurable week spent with my daughter in the Midlands and my son in Wales and their young families was utterly ruined. I was a nervous wreck from having to sparingly drive a car that was not fit for purpose and could have let me down at any time.
To add insult to injury, I note you have taken £18 from my account to fill up the rogue car which I was in no position to do.
Please find a report of the experience and note I shall be taking legal advice to ascertain what level of damages I should be entitled to claim.
Response received today offering no compensation.
Report was as follows (can be sent in more easily digested Word format if you send me a link):
Monday 8th
10.20: Fiat 500 WR15GGY picked up from E. Midlands airport
Wed 10th
15.00: Travelling south on M6 and stopped at services south of Birmingham.
Turned off engine.
Returned some 10mins later, started car and pulled away.
Drove onto slip road on to main carriageway.
Realised there was no power when tried to accelerate away although engine was still running at tickover speed.
Pulled onto hard shoulder and turned off engine.
Waited a couple of minutes highly disturbed by the passing of heavy vehicles.
Tried again to start the car – this time successfully with power returned.
Various warning lights came on and went off except one.
Proceeded cautiously onto M5 and onto M4 not daring to stop.
17.30: Reached end of M4 and took Ammanford road.
Within 3-4 minutes car lost all power again on steep hill and in heavy traffic.
Pulled over into a driveway and turned off engine.
Waited a couple more minutes and started car again and reached destination. (Son’s house in Llandyfan.)
Thursday 11th
09.30: Called Swansea branch and reported problem – they suggested calling AA
11.10: AA arrived – checked car and couldn’t find obvious fault.
Advised it was probably OK to drive to a garage but strongly advised against driving any distance and especially not on motorway.
AA man called Swansea office (spoke to Rob) and was informed no replacement vehicle available.
Then he tried Cardiff Airport, Cardiff City Centre, Newport and Bristol and given same message.
He phoned Fishguard who could have supplied a car but refused on the basis it would leave them short.
AA man commented on the appalling level of service, but said there was nothing more he could do and left.
13.00 Phoned Head Office
Was given phone number 01132.853450 for East Midlands Airport office which turned out to be a private number.
Found number 0843.3093024 from internet – called but no answer.
Called second number given by HO – 07912.284732 (told to ask for Jonathan). Received indistinct recorded message and had to call four times before could get the gist which was that he was on holiday until 15th June and to call 0***-***-**** and speak to Joanna (something)-Smith.
Called that number and was told she was not in the office, explained problem – was given yet another number 01269.269705.
In total made 15 calls to various numbers including Customer Services:
0121.7828950
07912.284732
0843.3093024
0843.3093029
01132.853450
0843.3093103 (###) ###-####3369
0800.7365.3369
0870.8448844
These had to be made at great expense from a mobile phone and on a number of occasions was presented with options that did not cover my situation.
17.00 Spoke to Birmingham office.
After lengthy conversation was informed there would be a car available in Birmingham on Sunday in time to catch return flight from East Midlands airport on Monday provided the AA ferried me and the car to them. Offered no advice as to what I could do about immediate situation.
Friday 12th
09.00 Called East Midlands office – no answer.
09.30 Ditto
10.00 Ditto
10.30 Ditto
11.00 Received answer.
“What do you want me to do? I am all on my own in the office dealing with everything.”
Did however offer to phone around to see what could be done.
Heard nothing thereafter from that office.
14.00 Called daughter to explain predicament.
She called Swansea office and spoke to Rob who said he was in process of trying to find a car but hadn’t called for fear of raising false hopes.
Mentioned possibility of a car available by 5pm that afternoon which actually happened and the Fiat was taken away.