Thinking of going to Greece (islands) next May . Not sure if it will
be warm enough to swim in the ocean. Also, how are the ferry schedules
that time of year ? What airlines would be the best to fly from London to
Athens ? Thanks

It is a personal call. People coming from Northern Europe often swim comfortably after middle May in most Greek location. Water is a a bit too fresh for most people at the start of May. Most of Greek people don't set a foot in the sea before July : )
Specific location is very important. As a general rule, the more south and east you go, the warmer it is (for example Kos, Rhodes,Crete). Northern islands are heating up later in the season, that been Aegean (eg Lemnos,Chios,Lesvos,Samothraki) or that been Ionian (eg Lefkas,Kefalonia,Corfu etc). BUT depends also on sea currents, depth and many other local factors.
Ferry shedules are more frequent than winter, but not in full blossom as in high season. More shedules on late May rather than early May, and popular routes get more ferries earlier than less visited routes.
What means "best airline" to you, I don't quite understand this question?

We just returned from our end of May/first of June trip to Greece (Santorini/Naxos/Mykonos/Athens). I thought the water was cool but it felt good as the sun was quite warm for me already - 80's during the day - shorts weather. We drove around the south part of Naxos and the wildflowers were in bloom - just gorgeous.

The ferries between the islands we went to during this time did not have multiple departures but only one. That wasn't a problem but something to check to make sure there is a connection the day you want to travel.

We loved the temperatures and are planning a return for next May as it was so enjoyable.

Thank you for the replys. As far as "best airlines" just looking for an easy flight from London.
I think BA or Aegean or ???

I prefer Aegean Airlines, but BA is okay, too. The budget airline easyJet flies to Athens from London Gatwick.

Re best time to go: May for sightseeing, June for beach weather. It varies from year to year, but early May can still be cold in the evenings, while late June can be very hot during the day. Late May - early June is a happy medium, IMO. I will be going in late Aug - mid Sep this year, which is also a great time for Greece. At the end of summer water is at its warmest.

We were there mid-late May and it was cooler than we expected. Spent a few days in jeans and jackets. Next time would probably push it back a week to late May-early June so it's a little warmer (like everyone else is recommending).