Replacing HTML site with WordPress - SEO Implications


I built an HTML site for a client a 3 years ago. It is well optimised and comes number 1 on Google search for all their most important search terms.

She has recently contracted me to rebuild this site in WordPress. The layout and content will be pretty much the same, but she wants to have more pages and do blogs/ galleries/ videos etc.

I am just starting on this site and it will go live in January. We want to minimise any downtime.

My question is, by remaking the site on the same domain in WordPress, do I run the risk of losing the SEO?

Has anyone got any experience or tips on this?

Would it be better to keep the same HTML homepage and link this to WordPress? (this has been suggested by the client but I don’t think she will get a lot of the benefits of WP with a static home page).