If it helps, I have been watching Celebrity's testing requirements on a regular basis as we are going from Rome on 4th June. Until very recently, the guidance stated that 'the test must be supervised by a health professional, pharmacy assistant etc.'. The guidance has now changed and doesn't mention the test needing to be supervised. However, I have just looked for you here - Travel Requirements for Southampton Cruises | Celebrity Cruises. It states that testing for cruises from Southampton must be supervised.
In any case, we have booked supervised tests through Boots COVID-19 testing (boots.com). There are other providers available, including ones where you take the test at home but it is supervised via a video call.
I hope you get sorted and enjoy your cruise. Celebrity is amazing (once you are on board) following all the stress of testing etc.