I can give all the gory details separately, but this is the overall shape. Fly into Cancun airport. After clearing formalities exit the building, turn right and walk down past the end of the building to an area where buses park. You'll run the gamut of lots of people trying to sell you cab rides - be pleasant, firm and negative. Once at the buses look helpless and a bus company (ADO) official will approach you and will speak in English. Say you want a bus to Playa del Carmen. The service is fast and efficient, in a heavily air conditioned very modern luxury coach, and from memory costs about US$7.
You arrive at one of the two bus stations in Playa, the one right by the sea and next to the ferry terminal for Cozumel. Before you do anything else, go to the booking office and buy a ticket for Chetumal (the main town near the Belizean border). You'll need to specify which bus, and bearing in mind the journey takes 5 hours (and costs US$18) decide whether to stay overnight in Playa. I always do, as there's lots to do there (zilch in Chetumal). The bus I book is the 9:30am one, which works well at the other end. I'm assuming you'll be coming from the UK and will be thoroughly jetlagged and very tired, and also that it will be too late to complete your journey to Ambergris Caye that day.
I can suggest hotels to you. Next morning you need to get to the other bus station, which is four roads in from the sea and 5 or 6 northwards. Be there 30 minutes before scheduled departure. Buses leave approximately on time, and like the previous bus are heavily air conditioned - you'll actually need something to keep you warm. There are several stops where if you're quick you can hop off and buy refreshments - make sure the driver (who will speak no English) understands what you're doing so he won't leave without you.
In Chetumal you arrive at the terminus. Here you will be met by the Belizean taxi company you will have pre-booked (one of the details I referred to - I can advise). He will drive you to the border, will help so far as he can with formalities (that help can be invaluable) and will wait while you clear formalities. He will then drive you to the Corozal airstrip in time for a departure direct to San Pedro. Taxi costs around US$20, air fare around US$25. You will also need to have booked your flight with one of the two airlines that make the trip. At San Pedro airstrip ask a taxi for your hotel.. And that's that!
A nice thing about spending a few hours in Playa is that you can buy very cheaply things like tee shirts and cotton shorts (so no point in bringing them from England) and there is a superb Italian ice cream shop near the first bus station. You can walk everywhere - I always stay at an hotel between the bus stations, and the total walk between bus stations is no longer than 20 minutes. A pleasant place to unwind from the transatlantic flight. If Americans are reading this, they may well find their flight arrival time permits them to make the bus journey and catch the last flight to San Pedro, thereby making the entire journey in one day. Europeans should remember that flying via the US they also have to overnight - the journey can't be done in one day. Doing that in Playa is much more pleasant and cheaper than going to an hotel near a main US airport hub.
Something you could probably do, but I haven't any experience of it. If you find somewhere in Tulum to stay, you could get there directly after arrival. It's on the route to Belize and not too far from Playa. There you can look at Mayan ruins and dive with a variety of dive shops - maybe take a few days before continuing to Belize. If you stay in Playa there are countless dive shops, with the main attraction being the inland cenotes.