You can try, but to be honest most Universities will have given out most of their places by now. A quote from UCAS says;
"Applications received by the above deadlines are guaranteed to be considered by the universities and colleges. Applications received at UCAS after the deadlines, up until 30 June, will only be considered by the universities and colleges if they still have vacancies for the course(s) you have selected "
It depends on what course you are doing, but most courses or universities will have no spaces left. Bear in mind that universities don't get your application straight away, it takes a few days for UCAS to process it. Also, competition for places is extremely tough this year, so it's unlikely they will have many left. Pretty much everyone I know has heard from all the Universities, so I doubt any will have kept places when so many people applied before the deadline.
So my advice would be to go ahead and try, but don't get your hopes up, as most places will be taken. It's worth trying though, you never know, and you can always try again next year if you don't get a place this year
Good luck :)