Logging Time in a PtF aircraft.

You sure can – for example, it can be conversion training to this very type of aircraft.

The Q is going to be: what can such time be used towards? You can write anything in your own logbook – even Easyjet flights to Greece

If there is no useful credit for the time logged, there is no point in logging it.

As the owner is a FI, he should no the answer to the question! You can log any instructional time however; to be valid for use with an EASA licence it must be endorsed by the FI who gave the training AMC.FCL.050.
The ANO Art 42 also lists limitations regarding the use of Permit aircraft.

Am I able to log flight time as PUT in a permit aircraft (which I have no ownership of) if I’m flying with the owner who is an FI?

sounds like you are flying as a passenger and want to log the “flight time”, not “instruction” in which case you could only log it as a passenger.

Are you on insurance for the aircraft? Is the instructor logging the flight as P1, and you as Pu/t? Hands on controls means nothing.
I’ve flown and landed a Piper Cub. I logged nothing. The owner, who allowed me to handle it, presumably logged it.

I assume you are talking about a g- registered LAA permit aircraft in the UK.
The LAA document summarises the dos and don’ts.
So no ab-initio training. To be legal as a crew member it needs to be insured , so you would need to be a named pilot or there is an ‘open pilot’ endorsement on the policy.
It seems quite legal for a permit aircraft owner to allow someone else to receive continuity training on their aircraft if it doesn’t involve any kind of remuneration.

I’ve found that most insurance brokers (including Haywards and Visicover) will add a named pilot for little or no extra charge, so it’s worth asking.

Jacko wrote:

I’ve found that most insurance brokers (including Haywards and Visicover) will add a named pilot for little or no extra charge, so it’s worth asking.

May not even be a named pilot. I am not sure if there is any difference between PtF and CoA aircraft in that respect, but for a CoA one, Traffords included “any pilot under 65 years of age, over 150 hours logged, checked out on type, and with no accident history” in my policy at no charge.