And why does tesla get 8 years and unlimited miles out of battery packs regularly cranking out 5C (several hundred kW) when pedelec batteries die after two years and negligible miles? Evidently its not heat, and I think you've all established its not charging protocol.
I'll leave the battery choice for someone else to help, since I tend to not buy 'off the shelf' packs. I would however recommend sourcing from within the UK if after sales service is of any importance to you.
Tesla packs achieve such a long service life due to a number of measures.
Firstly, as NJS correctly states, they only use 20-80% of battery capacity in regular daily usage (unlike most ebike batteries, their BMS deals with this practice in the correct way).
Also, they use active (fan) cooling to keep the pack at optimum temperature.
Additionally, they also use pack heating to bring the cells UP to temperature when operating in 'ludicrous mode' This is to make sure that the pack has the lowest possible internal resistance (IR), so that it can dump HUGE amounts of power with the very minimal of cell degradation.
Lastly, since they own and control the entire cell manufacturing process, they can ensure very high levels of quality control.
EDIT: Ebike batteries have the additional problem that they are much more price sensitive and as a result, compromises are often made that stress the pack far more than is ideal. Also, we often hear of packs that have been left to sit for a long time without usage, which causes issues. Electric cars don't suffer from the same usage issues as they tend to get used much more frequently. When it comes to the majority of lithium ebike batteries, it's definitely a case of "use it or lose it"!