As far as I know you can only undergo a Greek Orthodox wedding if you are first baptised in the Greek Orthodox faith. I know two couples where one was Greek Orthodox and the other wasn't and the non-Orthodox half was first baptised in the Orthodox faith. In one case the wife-to-be acted as the godmother at her future husbands baptism.
I attended one Orthodox wedding where the best man and woman were not Orthodox and that was not a problem but they couldn't follow the tradition of being godparents to the first born because they weren't Orthodox.
It isn't absolutely necessary to be married at a registry office in the UK first but I would recommend doing so. It is possible to do the whole wedding in Greece but you will be asked for a shed-load of paperwork, all translated into Greek by a translator approved by the Greek Embassy and all notarised. That does not come cheap. It is much easier to do the legal part in the UK and just have a religious blessing in Greece.
If you do opt to do it all in Greece, normally the legal part of the wedding would be done at the town hall but I did attend one wedding where the relevant person from the town hall attended the wedding venue and performed the civil service there. They then went to the town hall a few days later and signed all the documents and collected the certificates.
The two UK weddings I've attended here were performed at hotels with an Anglican priest carrying out the blessing service. The reception was at the same hotel. In one case the parents of the groom, who live on Crete, organised everything themselves , which was a lot of work. In the other case the parents of the bride used https://weddingincrete.gr/
to organise everything and were very satisfied with the service they provided.