I guess it depends what part of NE England you're in, but wherever you are, you need to fly to Kos. (Can get direct flights from London, Manchester, Liverpool, Edinburgh, etc.)
Once in Kos there will be an army of taxis waiting to drive you down to the ferry port. There is one evening ferry which waits for the flight, so if your flight is delayed, the ferry waits, don't worry. (It needs your custom!)
A quick 35 minute ferry ride and you arrive in Kalymnos where another army of taxis will be waiting to drop you at whichever hotel you have chosen. It is a tiny island, so all the taxi drivers know all the places.
The two taxi rides will cost 15 euros each and the ferry is 6 euros.
It really is a very quick an easy journey - and you will be surrounded by fellow climbers the whole way, so no risk of getting lost or anything. They really look after you!
Feel free to ask me if you need to know anything else.
Rest assured - you will love it!!!