Does the Golden Visa allow us to remain as full tax residents in UK?

Your global income still gets taxed under the law that allows you to live in the country on a permanent basis per year. In Greece, if this is not your tax residency, you are obliged to declare the property you obtained in the country at your annual tax declaration.

The Greek Golden Visa Program does not require a minimum stay in the country. As a Golden Visa residence holder, you are not considered as tax resident of Greece in any case, except if you spend more than 183 days per year in the country. Tax residency is an absolutely different issue from Golden Visa residence permit. The only tax that you are obliged to pay is for income generated in Greece if any, and for your property. But besides the above, I would like to bring to your attention that Greece has recently adopted very favorable tax provisions for those who are interested in transferring their tax residency in the country.

Yes, of course, you can remain UK tax residents.