Yes indeed, it is possible for a young driver over 19 to buy car insurance for one single day. You can apply for insurance for a car at any time using your smartphone, tablet or computer at any time provided that you have the vehicle's registration details and your driving licence particulars to hand.
It should take no more than a few seconds to get a quote. If you are offered one and accept it it takes only a few minutes more to buy a policy online. Your documentation would then be available for download very shortly afterwards if you wished to do so.
Your insurance policy can start immediately if you wish, or you can book it ahead if you prefer. If you buy a single day policy you get a full 24-hours of cover so it doesn't matter what time you buy it.
There is of course no guarantee, as with every other standard insurance policy, that every applicant would be accepted. Whether or not to offer cover to a particular motorist depends as always on the usual criteria such as driving experience, offences and accidents if any, postcode, type of car etc. There are certain inner-city postcode addresses that no insurer in their right mind would touch with a barge pole and to be realistic no underwriter would be terribly happy about giving a young man with six months driving experience a comprehensive policy on a modified Ferrari with twin turbos but if you live in a reasonable area and have a clean (or even clean --ish) driving record; and the car that you wish to insure is a fairly popular model in a low insurance group there is a fair chance that you would be able to get covered.
Either way it only takes a minute so to find out whether or not you would qualify so why not click the button at the top and apply for a one-day cover quotation now.