I agree fully with David, that you should work back generation by generation, if there is the sslightest hope of making any accurate connections.
Even if you find that someone has already traced the particular line, you should cross-check by following through.
The name CLARK originated as an occupational or possibly more accurately as an "ability", ie it was a person able to read and write - and as the early ones usually belonged to a religious order, it is a modified form of "cleric" etc.
Thus it could arise in a widespread manner anywhere almost.
An alternative name for someone with those skills is SCRIVENER, more directly meaning reading and writing clearly descibed as being a "scribe".
In the 1881 UK Census, CLARK is widespread in Scotland, down the east coast of England, with a concentration around Chelmsfor in Essex.
For comparison, SCRIVENER is mainly to the north east of London and much less widespread.
ALEXANDER is such an ancient name, used over large areas of Europe, that it is more difficult to summarise it.
Again in the 1881 UK Census, the last/surname use is concentrated in Scotland, with small amounts to west and south-west of London; and also a very small amount in East Anglia.