Traditional but not common

Verity
Josephine
Patricia
Margaret
Alexandra
Gabriella
Natasha

Josiah
Rupert
Tristan
Edmund
Peter
Joel
Duncan

Just coming by to say that today I heard a mum call her little girls name- Josie! She can't have been more than 3, never met a Josephine/Josie under 50 but it's a lovely name.

Gertrude nn Trudy
I don’t actually know any little Elizabeth and there are loads of lovely nicknames (Lizzie, Beth, Bethany.)

Sidney and Bronwyn

Lydia is lovely! What about

Constance (Connie)
Elspeth
Frances
Harriet

Owen
Hugo
Rowan
Xavier

Alexandra

She'd be the only one or two in the school. Lots of nicknames.

Boys - old classics due a come back
Mark
Luke
Robert
Peter

Heard of but not super popular was my criteria too . I went with Georgia for my first, though I like Georgina too. She’s the only one in the school.

Hester, Viola, Emmeline, Dorothea, Rosamund. Edmund, Edwin, Peter.

If you don’t like Maddie, then maybe Magdalena (Magda or Lena) might be an alternative to Madeleine.

Boys -
Theodore (teddy)
Lucas
Sebastian
Christopher (Kit)

(I find boys names harder to choose 😂)

My daughter Louisa is the only one in her whole school of 400 pupils.
Her nickname is Lulu. We always get lovely comments on her name. (Which I know people also do that just to be polite )
But it’s a name that suits all ages, travels well, is traditional but not common, has a cute nickname!

We also have a Hannah. She is the only one in her year group. Think there are 2 more in the school.
We like Emmeline if we have another- nickname Emmy.
My friend has a DD called Verity. Nickname is Vee. I think that’s a lovely name that you won’t find many with.
Other suggestions-
Flora (Flo)
Juliet (Ettie)
Susannah (Suzy)
Jemima (Mima / mimi / Jem)
Claudia
Lydia

Conrad

All your names are popular here!

When I think of traditional, but not too common, I think of:

Louisa
Annalise
Yvette
Bethany
Kirstie
Kristin
Jacinda
Miranda
Nadia
Celeste
Estelle
Haidee
Kate
Rhiannon
Tabitha
Ursula
Josette
Maxine

Kurt
Lincoln
Gareth
Ewan
Fraser
Christopher
Kane
Logan
Ryan
Stephen
Dion

Aw, sorry didn't see you already have a Lydia 😊 it's a lovely name! Congratulations!

My personal favourite names for a boy:

Andrew, Robert or Edward

For a girl:

Elizabeth (as it has so many variations - it's my daughter's first name). Her middle name is Amy (not my personal favourite but also quite lovely). I also really like Helen or Lucy.

Names in my immediate family (we all like traditional names):

Girls:

Anna
Elizabeth
Isabella
Elena (we're foreign so that's the spelling, but I would choose Helen)
Lucy
Anastasia
Sophia
Catherine

Boys

Victor
Alexander
Michael
Boris

All of the names you mention are very popular - Madeleine less so than the rest, but it’s certainly not unusual.

Caroline, Jane, Jean, Frances, Honor, Mary, Margaret, Genevieve, Lois, Susannah, Agnes, Augusta, Louisa, Flora, Katherine / Patrick, Robert, John, Richard, Duncan, Douglas, Christian, Marcus, Saul, Jerome, are all quite traditional but not used much right now

In terms of 'popularity' I do think names must be more / less popular in certain areas - be that geographical or economic or some other divide? So a name might be listed as top 10 or top 100 but, no-one in your 'circle' or your family, or, when they get there, their school might have that name.
I often read on baby threads about a particular name being really popular and think I've never met one

Violet nn Lettie/Lottie - It's pretty. I like nn Lettie
Matilda nn Tilly - Love this. My favourite on your list.
Alice nn Lissie - One of my daughter's middle names. I don't know many.
Madeline we dislike Maddie - Madeline is pretty. I think it's fine to use the full name.
Annie - I've always liked
Felicity - I've grown to really like this and it's not too common.

Others I really like -
Rosanna - nn Rosie (or you could have nn Annie)
Caroline - nn Carrie or Callie

Isaac - My favourite. I have one myself.
Jasper - Love this. I've never met one.
Joseph - Traditional but I don't know too many.
Benjamin - I like Ben.

John

Miranda
Rosalind
Rosamund
Alexandra

We are calling DD Alma after her great gran

I know an Alicia (ah-liss-ee-ah) who goes by Liss and Lissie. I think it's a really pretty name and a less popular alternative to Alice.

Everyone has their own cut off for 'not overly popular' - for me it's anything outside of the top 100. It's worth checking the top 1000 to see where the names you like fall if popularity is important to you. For example Annie is 115 in E&W and Felicity is 100. Madeline is 443 (Madeleine is 297).

A few suggestions:
Caroline
Sarah
Victoria
Serena
Naomi
Verity
Cassandra
Juliet
Louisa
Evangeline
Gabrielle/a
Francesca
Rachel
Katharine
Natalie
Mary

Francis
Peter
Patrick
Laurence
Alistair
Christopher
Dominic
Robert
Edmund
Philip
Nathan
Lewis
Eric
Nicholas
Joel
Robin

I think Sally deserves a come back