The next time this happens, simply tell them that they have no right to photograph beyond what was agreed, and instruct them to cease immediately. If they feel differently, it is up to them to demonstrate on what grounds they may photograph.
Secondly I would advise contacting a helpline and asking them - Shelter or citizens advice bureau.
Generally, at least in the US (every state differs slightly) a landlord or their agent can enter your apartment only in an emergency circumstance or with your explicit permission after requesting. The only time they'd take photos is after you've moved out to photograph damages for evidence if they with hold any part of your deposit. Your landlord should not be snooping around your house every 90 days, that's ridiculous. In the US, it's common to change the locks on the door after renting and then turning in the new keys when you leave.
It is also during period inspection, so they have asked to attend and it has been agreed.
However, isn't that their problem, not mine? Are they really using people's data to prove their business obligations?
They win elections with media support, even when taking opposite stances day to day because the people that own and run those media companies... Went to school with them.
It's like a big club, and most of us ain't in it.
But if you are in it, you can be stupid, lazy, incompetent or even outright evil and still succeed, aka, fail upwards.
Only to wealthy privileged people who can discuss their first-world problems on forums like this. As folks get poorer on the scale the more a car becomes an unavoidable necessity for many.
I applaud to your personal choices and sacrifices, but please don't make it sound like everybody can and should make the same/similar ones.
Most of us here have/want kids. I say something very opposite to what you say - folks here, please have kids! Not many, but take your time and raise them properly. It basically means sacrificing large portion of your life to them, without a guarantee they will even appreciate it. Which is fine, that shouldn't be the motivation for it anyway.
You who are reading this, are a part of smart elite in this world, whenever you are, and can raise next generation of elite with disproportionally large amount of decisive powers in their hands.
Why, you may ask? Raise them well so they are balanced happy individual with clear drive to help make this world a better place, and they may very well become next leaders, business captains, politicians, or just good citizens helping those around them, environment, mankind.
Now imagine what kind of world would that kind of attitude bring. Don't just minimize your 'bad' footprint on this existence, try creating more of the positive one.
My neighbor has five to seven cars on their driveway. To let others out they start them all and play musical cars. Two of them drive to jobs less than two miles away. They use them for practically every trip over 200 metres. Their extended family visit every weekend, in separate cars and all live within five miles.
My other neighbors have three cars for two people, including a pickup truck. Again, they drive literally everywhere. Even walking distance.
Many of the young people here drive terrible modded cars up and down all day for no actual purpose than vanity.
If you tried to have to have a conversation with these people about their car use, they would claim it's their right and that they "pay for it". Yet what they pay is < 10% of the damage they cause.
Obviously, if you are remote, or have a disability or need to carry a heavy load you should probably use a car.
But many people think it's literally their God given right to drive a dangerous metal box, badly, burning irreplaceable oil, spraying pollution, noise pollution and brake dust literally straight into your home.
Every single car journal under 10 miles should be excessively taxed, with extreme taxes for trips under three miles. You should literally be forced to think twice, then twice again.
All of these people are literally saying: "Fuck other people's health, their sanity, their happiness, their time, their environment, the environment as a whole. Me drive metal box"
The entitlement of drivers is literally staggering.
Per GDPR, they have an obligation to inform you what data is being collected and for what purpose (Article 14). If they only mention damage photographs, then any photographs that aren't about damage would have been collected unlawfully and you can request they be deleted (Article 17, in particular part 1-d). You also have the right to receive a copy of all data about you (Article 15), and I doubt that any of the usual exceptions apply to this case.
While you can infer so-called Special Category data (sex, sexuality, health conditions), I'm not sure it technically counts as Special Category data on its own. However the inferability of Special Category data should have been part of the consideration of whether this data collection is acceptable.
If the data is transferred to a cloud service, they are obligated to inform you. If this transfer is international, they are obligated to inform you what is the legal basis for the international transfer (but not the actual destination country). If they have told you neither, they are only compliant if the data is entirely on-device or on-premise.
You can file a complaint with ICO, the regulator for the UK.