I used the BBC pattern link to get the colour sequence - it is a knitting pattern.
My scarf is 11” wide and to get this I made 44ch and did rows of sc, starting the first row in 2nd ch from the hook and working a total of 43 sc across. At the end of each row I ch1 and turn making my first sc in the same stitch.
I reckon a row of sc gives me the height equivalent of two knitting rows so I halved the rows to be worked (eg, we start with 8 knitted rows of purple, so I crochet 4).
I introduce a new colour by pulling the new yarn through the two loops of the final sc of the previous row where an even number of rows are worked.
Where we have an odd no of rows in a particular colour, I FO the colour and join the new yarn at the same end as we started.
Starting each colour on the same side means that we have a consistent look for the whole scarf whenever a colour changes.

By the end of the knitting pattern my scarf measured 228cm (90”). I didn’t think that this was long enough, so I added further colours as per charts I found online as follows using the colour terminology consistent with the BBC knitting pattern (Stylecraft colour in brackets):
8 Camel (Stone)
5 Purple (Emperor)
16 Bronze (Walnut)
5 Rust (Tomato)
16 Purple (Emperor)