Well you can't leave Europe without having been to the Greek islands. You have three choices probably due to time constraints, but I will make an assumption that you will be traveling whenever you get time off work. So if you get 5 days off combined with two weekends you could the following.
1) Aegean islands - The Cyclades
2) Crete
3) Combine two islands for that time period in the Ionian
Crete is huge and realistically you need two weeks to get a feel for the island. Same applies to the islands in the Ionian. Large islands with much to see. Thus I will suggest a bit of island hoping in the Cyclades, with a mix of well known and less known, at least to non-Greeks.
I have made this recommendation in the past to friends for many reasons. The islands in the Cyclades are small, and you get the feeling you are on an island all the time. They are easy to get around, have stunning small villages, nice beaches and a very different vibe compared to Crete and the Ionian.
I would get a direct one way flight from the UK to Santorini and spend two days there. It is expensive, but it is rated as one of the best places to visit in the world. I would avoid eating at restaurants or taverns here. Eat simple, i.e souvlakia, pitas etc, and save your money for eating out in the less commercialized islands below.
I would then go to Amorgo for two-three days. The Big Blue was filmed there and has become a bit popular over the past few years with the 20-30's that avoid over commercialized islands. The Chora (Main Village) is great with friendly people. The local specialty is raki psimeni, or Amorgiani. You might have tasted raki in a Turkish restaurant in London, but this is different and is served with honey or the local version with spices. Don't get fooled by the taste, it is almost 30% alcohol. The camping site on the island is popular and has good facilities if you are into that.
Next stop for two days, Koufonisia. The island is small, you can walk around it in an hour! The Chora here is small, nothing like Amorgo's or Santorini's. The island has become popular with the young professional crowd 25-35 who want to get away from reality for a few days. The island has a few small cafes and restaurants and ONE bar! The food on the island is amazing. It is probably the only place in the Aegean where you will not pay prices for fresh fish comparable to gold. The island is well know for its fishermen and thus the few taverns - restaurants will always have fresh fish. From the Chora you walk to the beaches or take one of the small fishing boat taxis...
For your next stop I would let you decide between Paros or Folengadros. Depending on which of the previous islands you preferred you would make your choice. Folegandros is like Koufonisia whereas Paros is like something in between Santorini and Amorgos. Unless you are traveling in August you should be able to find accommodation upon arrival.
I would leave by taking the ferry to Athens, stay there for two days and get a flight back to London. Athens's centre is full of history and activity. If you do ever decide to make it I would happily show you around the local spots in the center and give more specific details for the islands, i.e. where to eat, stay, tips etc.
The islands in the Cyclades are interlinked with ferries so getting from one to another is relatively easy. You could do all the above in 10 days.
Pictures of Koufonisia
Pictures of Amorgos
Santorini
http://www.greeka.com/cyclades/paros/paros-pictures/members-1.htm