Name change for this, as outing.
I inspect care homes and the domiciliary care contracts for a local authority. It is a nightmare and there is no way that we can keep up with the complaints. I lose loads of flexi every month and work over most of my lunch breaks as we are constantly swamped.
Definitely report this to the CQC as even if it is all resolved, they would still be able to keep this information on file. It will inform their view of the care provider and the carer involved.
Report this to the care manager in the Social Services department and the Commissioning Section too. Does she also pay the Council for her care, or directly to the Dom Care company? If the former, your friend should have the support of the Council and Commissioning / Contract Management should investigate the complaint. They may also be unaware that carers can circumvent the clocking arrangements and this information would be useful to them even if your friend's contract with the care provider is independent of the Local Authority.
Many companies turn a blind eye to their staff working in this manner and even encourage it sometimes. If the company is being paid £15 for seeing Jane Smith for 30 minutes and another £15 to see John Jones for the same duration directly afterwards, there is no time written into the equation for travelling. This cuts down the time available for actual care but (depending upon the contract arrangements) the LA is being conned out of the full amount. If it is a private client, that person too is being charged for time where no care is provided.
The care company can also 'double book' a carer's time. The council and / or private clients will pay for the full hour (if two sessions of 30 minutes are involved) between them, but if the carer can squeeze in another client over the same hour, the £30 payment to the company will be increased by the extra fee charged to client 3, whether Local Authority or private. One company (eventually sacked from the contract) was allocating a carer with up to 2.5 hours of work in one hour, for clients living in the same block of flats. They did this with a number of carers each day, enabling higher charges to be levied against the council. The more sinister aspect of that was that vulnerable clients who needed support and medications prompts were receiving very little or no care.
I'm absolutely not saying that the carer involved is working to the instructions of the care company, but it is a factor that needs to be considered.
Carers can behave indescribably badly, especially if they believe that they have found a soft and vulnerable target. Thankfully, most carers are not like that but even some apparently 'good' carers can be pretty shocking. We often receive whistleblowing complaints from carers, raising concerns about their company or other carers.
Another issue is that clients usually don't want to complain. They even lie through their teeth to protect a favourite carer or even just because they feel afraid to reveal what has been happening. One carer was notorious for wearing a 'birthday girl' badge every few months to encourage clients to give her money. The same carer used to wash and set the client's hair, make her lunch and sandwiches for later, wash, dry and put away the dishes, vacuum, dust and do the shopping, all in two 30 minute sessions daily, none of which were ever missed. The client absolutely adored the carer and spun yarns galore to protect her. Of course, the carer did very few of those tasks and regularly missed visits to this severely disabled and blind client. The carer was reported by another carer who had just been on safeguarding training.
Take copies of visit documentation and any Meds Record sheets. One of the companies I dealt with used to forge signatures in any gaps in the records, when the paperwork was collected. If the copies are taken after each visit (as much as possible!), it also prevents the carer being able to back-fill details at their next visit.
The government, police and CQC do not recommend the use of covert recording equipment, but I would not hesitate to use it if I had any suspicions. One carer(much loved by the client) used to hand the client's purse to her for shopping money. All was apparently above board. The hidden camera installed by the family who were curious about the amount of money being spent, showed exactly how the carer stole the cash in full view of the client.
It's a minefield. Thankfully, there are so many more fantastic carers than bad or criminal ones and 
to those hardworking, decent and dedicated people who do an indescribably difficult job under some grim and stressful circumstances.