Is there a legal way to appeal on A-level art project grades?

Simply ask the HoD to have the coursework moderated. If there is a big issue like you say, it will be fixed (yep, another teacher here; yep, I'm sure that's how it works).

I would bet a large amount of money that you are deluded about this one:

"just to mention: the teacher's daughter applied to UCL and Edinburgh last year and failed, and this can be the reason." Do you know how batshit this sounds?

"the head of art department in the school says that my daughter deserves A" If the HoD thought all the pieces were A grade, she'd have been given an A* for them, because the HoD is the boss. Either the HoD is too generous (ours was when he first arrived) or, more likely, you are twisting some offhand comment.

When your daughter doesn't get an A* because the moderation stuck with the original grades, I think you should consider the impact your behaviour will have on your children. Growing up with unrealistic expectations and an overactive sense of entitlement isn't healthy.

Anyway, even if internal moderation doesn't work, there will be external moderation, which marks work independently of the school. Both the teacher and the HOD will be hauled over the coals if a big adjustment is required.

So, the teacher's own HOD has told you that she believes the teacher has marked incorrectly, but the mark still stands??

Just to echo a PP there is no way the art teacher will mark your daughter down... the teacher needs her students to get the very best marks as it's a reflection on her. To suggest she's marking it down due to jealousy is absolutely absurd.
There will be criteria her work has to be marked against and maybe she is creating great art that just isn't hitting the specific criteria.
Also, who are these art professionals giving their opinions? Do you think they're being truly honest or are they placating you? Family friends??
If you're really concerned ask for it to be moderated

I call early April fools, surely no one is this bonkers?!?!

I think your crazy if you believe the art teacher is jealous of your daughters uni offers

Are there any legal means how we can influence the teacher?

no of course not.

you are being ridiculous.

Any attempt to influence the teacher is likely to result in your daughter being disqualified from A levels, and she may have her GCSEs taken away from her too.

As a teacher her appraisal, pay, career are based on getting the best grades she can. No way is she marking your daughter down 3 grades because she's annoyed she got into the uni her own daughter didn't.

The art teacher's daughter has nothing to do with this. If you think it does, then you are likely to be totally wrong about that,and if you are so wrong about that, you are likely to be wrong about other aspects of this story too.

I don't think you are in a "silent" conflict with the art teacher, I just think you are disappointed with her grades.

Professional opinions mean very little, it is how she fares against the criteria that the exam boards sets out that matters.

Art teacher deliberately marking her down through jealously??? This is a non issue. Its not happening, and if it were, it would be picked up by internal moderation, and if the internal moderation was inadequate,that would be picked up by the exam board.

Your real question is what can I do about my DDs disappointing art grades.

the answer is speak to the teacher and ask for constructive feedback (DD, not you, obviously). And contact the head of art and ask them to confirm they agree with the marks.

(politely, without spouting off about the art teacher's daughter!!! - cos that makes you sound bonkers)

I think that schools can ask for re-moderation by the exam board if results for a whole class are below their expected grades. But am not sure if this can be done for just one candidate (I suspect not as it could affect other pupil's grades).
I will not give here too many details, but just to mention: the teacher's daughter applied to UCL and Edinburgh last year and failed, and this can be the reason.
This shouldn't be relevant to your daughter in anyway.

the head of art department in the school says that my daughter deserves A, but the art teacher keeps marking her projects B and C.*
Could it perhaps be the case that the Head of Art is being a bit too generous and the teacher a bit too strict and the approx grade is A? At this stage any grade given for coursework is very provisional as no-one knows exactly where the grade boundaries will be, these vary annually.
It depends on how many pupils the sixth form are entered for Art A level but the exam board does externally moderate coursework. For Art subjects the examiner usually comes to the sixth form to view the portfolios. This may be all of them if only a small number of candidates but a sample for a larger number. In many centres the work may be moderated internally as well e.g. by Head of Department or another teacher.
Teachers have to go on courses about how to assess coursework. The final marks may be moved up (or down) by the external moderator if needed.

You need a meeting with the head of department surely?

sorry, meant ask for the exam board's grounds for appeal for internally assessed coursework - there will be guidelines.

Contact the exam officer at the school in writing and ask for the school's procedure for internally assessed coursework plus the school's appeal procedure/grounds for appeal.

Are the projects not internally or externally moderated?

The exam board can request wirk for moderation & will adjust accordingly. I would say your first port of call would be to raise the matter informally with the head of art, & if you get nowhere put in a formal complaint to the head teacher.

I would be expressing concerns to the head of department in the first instance. Work should be internally and externally moderated to ensure consistency of marking and fairness.

Ask the school for your DD's marks to be moderated.