Alfred the Great (he of the burnt cakes) is generally taken to be the first King of England. His grandson Aethelstan was the first to claim that title, but who's heard of Aethelstan? Nobody, so we'll say Alfred. It all works out the same anyway.
The line down from Alfred was broken a couple of times by the Vikings, but managed to make it through nearly to the Norman Conquest in 1066. Harold Godwinson (he of the arrow in the eye) was not the closest heir to Edward the Confessor - that honour went to Edward the Exile, the Confessor's nephew.
Obviously, the Conquest broke the chain of Saxon kings - but it's possible to trace their lineage quite a lot further. (In the tree below, the hypothetical line of succession is numbered. Historical monarchs are bolded; other members of the hypothetical line are italicised. Only children and spouses relevant to the succession are listed.)
Margaret was proclaimed Queen
of Scotland, but never set foot
in the country, and was never
crowned.
Alexander
1264-1284
David
1272-1281
Margaret
1193-1259
== Hubert de Burgh
Megotta
1227-1237
Isabella, Countess of Norfolk
1195-1253
Marjorie
1200-1244
David, Earl of Huntingdon
1152-1219
== Matilda of Chester
Had his daughter Margaret's
line died out, the succession
would have passed through his
younger daughter Isobel to
Robert the Bruce, and ultimately
to James VI & I of Scotland & England.