These are the type of thing they grow at the Eden Project. They are from South Africa so will need year-round greenhouse treatment. And warmth over winter. They need a well-drained soil with low nutrient levels, so don't feed them. Mix sand and grit and compost together to make your own potting medium for them.

They must have been on their holidays, as all of my info. says that B. hookeriana is restricted to Western Australia...... : )
One of my friends in the Australasian Plant Society (which is based in the UK for people interested in growing Australian and NZ plants) has had good results with Banksia seedlings in 50% medium grade Perlite and 50% ericaceous compost in an open north facing cold frame in summer, watering with rain water. In winter, put in an almost frost-free greenhouse.
When growing on, don't let little (especially black) pots get too hot in summer and provide good ventilation.
Just one piece of bad news about B. Hookeriana - they are one of the more tender ones and can perish at -2 degrees....
I know of other Banksia varieties planted outside in the UK (in Yorkshire and Sussex). I usually buy mine as plants from nurseries. They are great and very architectural.

Have to agree with Longleaf. Banksia hookeriani is from Oz ... a very small spot in Western Australia ... we commonly call it the Australian Honeysuckle.

It should grow fairly easily from seed ... but it should be sown in good freely draining seed compost. Surface sow using an Ericaceous (Rhododendron, Heather, etc.) compost. The seeds should be sown in a propagator or warm place to maintain an optimum temperature of 70-75F (20-25C). They will need light.

Once they've germinated and are ready to be potted up ... make sure they are fertilized sparingly. As with most Banksias, hookeriana is super-sensitive to phosphorus. It is toxic to them. Their natural growing conditions are in nutrient-poor, very well-drained sandy soil, with little or no leaf litter ... so fertilize sparingly, if at all, but definitely with low-phosphorus fertilizer.

Have to repeat Longleaf's note about good ventilation too