Planning approved - make alterations

1). Yes. You can commence on the current approved plans. And a submit a change of plan with the council (they may require a new application)

2). Only to build aspects contained in the revised design.

We recently inherited some money and are now in a position to expand the scope of work basically a single story extension can now become a double extension to give us an extra bedroom but we will need planning for it.

I assume you mean a single story projecting wing/conservatory rather than an extension. But in case not, You cannot build an extension that wasn't on the plans during a new build, and if it is on the plans it's not an extension. But that does raise the other option, rather than applying for planning. You can complete the house, as per the plans, and then build the addition area as an extension.

Is the change going from a one story extension to a two story extension? If so I would think you could not proceed using the current planning permission and a new planning application would have to be submitted before starting any work.

It might be possible to submit it as a revision to the current planning permission depending on the nature and extent of the changes but there is no guarantee it will be granted so I wouldn't begin building until permission for the revised plans has been granted.

I'd only begin building if construction of the extension which has planning permission is largely independent of the proposed extra extension.

The current extension is approved. There no issue starting construction on an approved permission regardless of second application pending. The second can be approved or rejected. Neither outcome affects the existing grant.

Agree that the engineering requirements are different but most single story sections would have have over engineered foundations anyway.

And if the plan was/is a future upper extension. Then makes sense to design for that future case.