Reminder: London buses have gone cashless
If you are arriving in London for Loncon 3 (and/or Nine Worlds) in the next few days, please note that, in Transport for London's beautifully euphemistic language, London buses are now "cash-free". Or, in other words, you can now no longer use cash on London buses.
The easiest way to use London buses is with an Oyster card with a large enough cash balance on it - a single bus journey costs 1.45 GBP, which you have to pay again every time you change buses until you reach the daily fares cap (more details below). After that, further travel that day is free.
A "contactless" credit or debit card can be used instead of an Oyster card - if you have been issued with a credit or debit card from a UK bank during the past couple of years, it is probably contactless but otherwise it probably isn't (even if it is chip-and-pin).
Otherwise, there are still some pay-in-advance paper tickets that let you travel by bus, but these are either Travelcards (day or longer-period tickets) or tickets from places outside London which include Travelcards. Paper single London bus ticket are now just historic memorabilia.
Also, if you are going to Nine Worlds and arriving at Heathrow Airport, most buses are free as far as the hotels around Heathrow Airport hotels (including the Radisson Heathrow), so the above doesn't apply until you need to travel outside the immediate Heathrow area.
If you have not got a Visitor Oyster card when you arrive in London, standard Oyster cards are obtainable (for 5 GBP) from tube and railway station ticket offices in London or from "Oyster Travel Stops" - several hundred newsagents and convenience stores in the Greater London area. Most (just possibly all, though I wouldn't guarantee it) will still accept cash and chip-and-pin credit cards - but don't depend on being able to find one quickly in a part of London that you don't already know. Or, for that matter, within a mile or two of Heathrow Airport (except for the ticket offices at the tube stations inside the airport).
Finally - daily fares caps. For travel only on standard London buses, anywhere in Greater London, this is 4.40 GBP, just over the cost of three single journeys. If you also use tube or rail, the cap depends on whether you first use public transport that day before or after about 9.30am and the zone furthest out from central London you travel through by tube or rail that day. Excel is in zone 3, Heathrow is in zone 6 - the cap out to zone 3 is 7.70 GBP after 9.30am and out to zone 6 is 8.50 GBP. If you use any form of public transport before 9.30am, the caps are 10.60 GBP and 15.80 GBP.
Looking at this, it is fairly obvious that the cheapest method for travelling from Heathrow to Excel with an Oyster card is by bus. However, I wouldn't advise it - I haven't found a route that requires less than four changes of bus (and at least four hours on buses), there is only limited room for luggage on London buses, and while I do use London buses quite a bit, they get distinctly uncomfortable after an hour or so.
The easiest way to use London buses is with an Oyster card with a large enough cash balance on it - a single bus journey costs 1.45 GBP, which you have to pay again every time you change buses until you reach the daily fares cap (more details below). After that, further travel that day is free.
A "contactless" credit or debit card can be used instead of an Oyster card - if you have been issued with a credit or debit card from a UK bank during the past couple of years, it is probably contactless but otherwise it probably isn't (even if it is chip-and-pin).
Otherwise, there are still some pay-in-advance paper tickets that let you travel by bus, but these are either Travelcards (day or longer-period tickets) or tickets from places outside London which include Travelcards. Paper single London bus ticket are now just historic memorabilia.
Also, if you are going to Nine Worlds and arriving at Heathrow Airport, most buses are free as far as the hotels around Heathrow Airport hotels (including the Radisson Heathrow), so the above doesn't apply until you need to travel outside the immediate Heathrow area.
If you have not got a Visitor Oyster card when you arrive in London, standard Oyster cards are obtainable (for 5 GBP) from tube and railway station ticket offices in London or from "Oyster Travel Stops" - several hundred newsagents and convenience stores in the Greater London area. Most (just possibly all, though I wouldn't guarantee it) will still accept cash and chip-and-pin credit cards - but don't depend on being able to find one quickly in a part of London that you don't already know. Or, for that matter, within a mile or two of Heathrow Airport (except for the ticket offices at the tube stations inside the airport).
Finally - daily fares caps. For travel only on standard London buses, anywhere in Greater London, this is 4.40 GBP, just over the cost of three single journeys. If you also use tube or rail, the cap depends on whether you first use public transport that day before or after about 9.30am and the zone furthest out from central London you travel through by tube or rail that day. Excel is in zone 3, Heathrow is in zone 6 - the cap out to zone 3 is 7.70 GBP after 9.30am and out to zone 6 is 8.50 GBP. If you use any form of public transport before 9.30am, the caps are 10.60 GBP and 15.80 GBP.
Looking at this, it is fairly obvious that the cheapest method for travelling from Heathrow to Excel with an Oyster card is by bus. However, I wouldn't advise it - I haven't found a route that requires less than four changes of bus (and at least four hours on buses), there is only limited room for luggage on London buses, and while I do use London buses quite a bit, they get distinctly uncomfortable after an hour or so.