Romans

Sparks is a series of historical novels designed for Primary Age children.

A Circlet of Oak Leaves (1968) and Eagle's Egg by Rosemary Sutcliff 1981, In Eagles honour Set in the C2nd
A runaway donkey (Sparks)
Between the forest and the hills by Ann Lawrence. The Romans have left Britain but one group is left behind.
Boudicca strikes back (Sparks).
Eagle of the Ninth by Rosemay Sutcliff 1954. A Roman soldier is injured and has to make a new life for himself in Britain.
Eagle’s honour by Rosemary Sutcliff
Frontier Wolf by Rosemary Sutcliff 1980. Set in Roman Britain
Lantern Bearers by Rosemay Sutcliff 1959
Legions of the eagle by Henry Treece
Outcast by Rosemary Sutcliff 1955.
Pompeii: The Diary of Claudia, Pompeii, AD 78 by Sue Reid 2008 (My story)
Roman Invasion: A British Boy, AD 84 by Jim Eldridge 2008 (My story)
Roman mysteries series by Caroline Lawrence. Set from AD79 the adventures of 4 children in and around the port of Ostia. Realistic depiction of the children's lives includes slavery and the violence of their society but in an unfrightening way. The first book is The Thieves of Ostia.
Roman Tales by Terry Deary Simple but fun stories for beginner readers
See You Later, Gladiator by Joe Scieszka 2000 (The Time Warp Trio). Three boys have access to a magic book that can take them through time.
The Capricorn bracelet by Rosemary Sutcliff 1973
The Eagles have flown by Henry Treece
The Great necklace hunt (Sparks)
The Guard dog geese (Sparks)
The Lost legionary (Sparks)
The Roman Twins by Roy Gerrard. Rhyming picture book about twin slaves who run away with a horse
The Silver Branch by Rosemay Sutcliff 1957
The Wadjet Eye by Jill Rubalcala

As well as books there is at least one board game with a Roman theme.
Albion is set in Britain at the time of the invasion. You are part of the Roman Army and trying to set up more settlements than your oppenents. It takes about an hour to play and is designed for 2-4 players. A good strategic game.

Scotland

Having just had a holiday in Scotland I was looking for stories set in Scotland which proved surprisingly hard but here is what I found.

The Boy with a Bronze Axe by Kathleen Fidler Set in the Orkneys this is about a stone age tribe and their first encounter with the bronze age. Gripping adventure
Eagle of the Ninth by Rosemary Sutcliff Marcus must go to Scotland to retrieve the lost eagle of the Ninth Legion. Marvellous historical adventure set during the time of the Roman Empire.
Hamish and the fairy gifts by Moira Miller A crofting family have to outwit the fairy folk. A beginner reader book.
The Hill of the red Fox by Allan Campbell Alisdair returns to Skye and solves the mystery of his dead father's estate
Katie Morag delivers the Mail by Mairi Hedderwick (and of course all the other Katie Morag stories) Delightful picture books depicting life on the Isle of Struay from the point of view of young Katie Morag
The Puzzle Ring by Kate Forsyth Hannah discovers that her father was Scottish aristocracy but there is a curse on her family and she must go back in time to the 1560s to break it. Starts in Perth and moves all around. As an added bonus Hannah is home educated.
Seal Island by Rowena Farre Rowena and her aunt moved to a remote croft in the 1930s where they managed to adopt a couple of seals. This is a true story.
Six Dinner Sid: a highland adventure by Inga Moore Picture book sequel set in the Highlands.

It is also worth looking on the Kelpies website as they republish children's books set in Scotland.