Traditional but not common

Helena
Anne
Adeline
Margaret

I don’t think any of your choices are that unusual.

How about

Naomi
Josephine
Jennifer
Stella
Emma
Zoe (although I’ve been coming across a few little ones recently)
Camilla

Edwin
Alistair
Matthew
Anthony
Patrick
Dominic
Malachi

Elizabeth (Betsy/Eliza)
Adaline (Ada)
Charlotte (Lottie)
Alexandra (Andi)
Sapphire (Saffy)
Fionna (Fifi)
Ruby
Getrude (Gertie/Trudy)

Another vote for Elspeth, I know only one aged in thirties. Rosalie? I know of only one aged in her twenties, the others I know are 40 plus.

People are saying the names OP gave are very popular but Violet for example is ranked around 50th so I wouldn’t class that as very popular.

The most popular names are given to less than one percent of babies. There's only 30 in a class. 30-90 in an average Primary year. Approximately 200ish at Secondary. Mathematically, you'd expect no repeated names in a class, or a Primary year, and maybe one other at secondary.

One of my DDs has a top 10 name. In two nurseries and five Primary schools, never had another in her year with her name. Or her swimming class, scouts, sports clubs...
My other DD once had 5 boys with the same name in her preschool/reception mixed group of 40, or which 15 were boys. It wasn't even a top 100 name. None had been born in the area...

I like traditional names, but I wouldn't care if they are common or not if I liked the name.
Lydia is lovely and doesn't seem to have jumped on the popular train just yet. Or Georgina/Cecilia etc.

Laurence
Wilfred
Nathan
Seth

Verity
Jemima
Clementine
Audrey

I think you need to go less commonly used for babies these days than your current list. Maybe the 1970-80's baby names? e.g.
Victoria
Elizabeth
Sarah
Claire
Caroline
Diana
Kerry
Emma
Matthew
Simon
Adam
Scott
Craig
Richard

Sorry but...

I know 3 Violets and 3 Alice's. Matilda seems to be the most popular girls name in my area. I don't know any Madeline's but lots of similar Madeleine's (though only one baby). I don't know any young Annie's, but do know of 2 young Felicity's. Basically these are all quite popular names but especially Matilda.

For your boys Isaac is very popular and I know of quite a few Jasper's too. Benjamin and Joseph are both consistently popular throughout the years.

All lovely names but popular names. I think your best bet for no other children in their class would be Annie and Jasper.

Names that seem traditional but uncommon

Michael
Dominic
Alistair
Robert
Peter
Patrick
Nicholas
Hamish

Angelica
Rachel
Jacqueline
Natalie
Patricia
Ruth

I have a boy and girl from your lists - my daughter is the only one in her school (450 children) and at her clubs, my son is the only one in his year, at his clubs. I’ve never met another child with their names

OP, all the names you mentioned are VERY popular nowadays for primary aged children. Those names are in every single class. If you want some less popular but traditional names then I would not look at Biblical names or names popular in the Victorian era (all your names can fit in these categories).

I would say that popular girls names from, say, the 1960s are not that popular nowadays so maybe go for those? Biblical and royal names are always popular so avoid these.

Caroline
Dorothy
Harriet
Gemma
Miranda
Nora
Clarissa
Lara
Briony
Rachel

Fred
Marcus
Jeremy
Edwin
Gregory
Owen
Christopher
Tristan

Edith
Bryony
Tamsin

Conrad
Torin
Elias

There's bound to be at
least one other Joseph, Benjamin, Isaac or Alice within the year group.

I guess it’s an era thing as my dC is year 8 has one sarah, in my day that was popular.

David
Barry
Gary
Dorothy
Dorian
Joanna
Lesley
Leslie
Penny
Ruth
Hayley
Ann
Patrick
Patricia
Kara
Sharon
Denise
Amanda
Tracy
Rachel
Louise
Sian
Isla
Kieran
Blake
Gary
Lisa
Michelle
Sharon
Ester
Claire
Simon
Andrew
John

Miranda
Clementina
Georgina
Channing

Hugo
Felix
Lawrence

Rosalie is nice and can also be shortened to 'Roz'

How about Alicia rather than Alice, I think it's less popular and nn Lissy comes more naturally from it?
From your others I think Annie and Felicity are the best options to fit your criteria.
For boys, how about Sebastian, Dominic, Matthew? I would avoid Isaac in terms of popularity.

Harriet
Lydia
Anna
Emmeline

Popularity is a really funny thing. My DCs both have names that were around 20-30 in popularity on the name lists when they were born. So quite popular, in theory. We’ve only met one other child with DC1’s name and know of one withDC2’s name.

You might like the following for boys:

Zachary
Seth
Edmund
Francis

For girls:

Violet, Alice and Matilda are all very popular (for good reason!). Felicity is a lovely name! I also really like Madeleine (I prefer this spelling).

How about:

Gabriella
Nina
Charlotte
Elspeth

Rosalind/Rosamund/Rosaline - Rosie or Rosa for short
Susannah - Susie/Suzy
Matilda - Tilly, Millie, Tilda, Mattie