Referring to "The Complete Motorist", by AB Filson Young (1904 edition)
"Petrol and paraffin oil should be kept in a separate building; the
roughest little cabin will do as long as it is thoroughly ventilated;
but these storesshould on no account be kept in any building adjoining
either motor-house, stables, harness-room, or the living quarters of
(presumably, in order of importance!)
If petrol is stored in the ordinary two-gallon tins, any rough outhouse that can be locked up will serve the purpose; but if it is desired to store petrol in bulk, special tanks will have to be constructed and a special licence obtained".
So, you generally filled up at home, and either re-filled your 2-gallon tanks at the dealer, or had a delivery to your specially built storage. But:
"But with the present facilities for obtaining petrol at short notice few motorists would find it necessary to store it in such large quantities"
So, even by 1904, this was going out of fashion in favour of filling up on the road. Even though valve seat grinding was something the driver was expected to do as routine maintenance.
As for who could afford a car, expenses are quoted as £84 a year, affordable by a country doctor, and indeed £50 cheaper than his previous horse and carriage! (Petrol was 1 shilling per gallon, for a 25mpg car, doing about 5000 miles a year on mainly local journeys)