i have worked at H samuals as well as it can be quite pricey.
From experience though most metal watch staps have a similar design. Each link is attached to it s adjacent links via a metal bar/pin which needs to be pushed out.
You have to remember to take exactly 2 links from separate sides to the clasp so the watch sits correctly, otherwise if you were to take all four from one side of the stap either the face or the clasp would be in the wrong place on your wrist.
As I already said the links are connected to each other via metal bars/pins usually only a few links either side of the stap can be removed as if you were to remove to many the watch would not fit correctly. The links that can be removed will have two indicating marks 1)arrows on the 'inside' edge of the watch strap which tell you in which direction the bars are to be removed and 2) the bars within those links are visable then looking at the side of the strap i.e they are not moulded over/covered for cosmetic reasons.