There should never be more than one NHS logo on a page.
As in the example here, where NHS organisations are working together in a formal partnership, an NHS partnership logo can be created.
As this is a website, there is the option to position the NHS partnership logo to the top left, as people often expect to see the search facility in the top right area of a website. The NHS logo and type underneath it would then need to be ranged left.
Alternatively, for non-formal NHS-only partnerships, a single NHS logo should be used and the names of the NHS organisations would be listed in text. These would be positioned outside the NHS logo exclusion area, preferably at the bottom of the page. For more information, please see the partnership branding guidelines.