With ACHIEVED grades there is no flexibility - ie. no question of you getting higher grades in August - so, for anywhere asking A grades, its almost certain that with BBC you will get a straight rejection, as that sort of Uni doesnt need to be 'kind' to anyone with a grade below in all 3 A levels. You
might get an offer for a course asking BBB but make sure you also apply for tat least 3 asking BBC.
Psychology is very competitive so its likely that Unis will not be dropping grades at Clearing and you'll probably only get offered places at Unis you could have applied to anyway (ie. asking BBB or BBC) or for unusual subject combinations (Psychology with .....).
Grade ranges (ABB-BBB) usually mean that the first grade set is the standard offer and the second one only for 'contextual offers' (those from disadvantaged backgrounds, low performing schools etc). So do not
assume you would be considered for the lower requirements - check with the Uni exactly what the criteria for the lower offer actually is.
Don't get obsessed with 'grade requirements'. A Uni asking for higher grades doesn't mean that its a 'better' course or that you will enjoy the course or the Uni more. Instead, look at the course content - what optional units are available in each year of the course, what really interests you and which ones would you actually choose, are there any opportunities for study aboard, work placements etc). This is all far more important for your enjoyment of the course, and therefore degree result, than the brand name of the Uni (employers are actually far less impressed wit this than many school leavers assume).
It IS worth looking at courses beyond just 'Psychology' as all joint subject courses have a higher application/offer ratio meaning are far more likely to get an offer even for those asking BBB. As examples : - Applied Psychology and Criminology at Brighton (BBB), Psychology with a whole range of 2nd subjects at Keele (BBB), Philosophy and Psychology at Aberdeen (BBB), Psychology with Developmental Disorders at South Wales (BBC), International Relations and Psychology at Plymouth (260 points), Education Studies and Psychology at Oxford Brookes (BBC). What Uni (
http://www.whatuni.com/degrees/courses/degree-courses/psychology-degree-courses-united-kingdom/m/united+kingdom/r/5973/page.html) is a good place to look for appropriate courses as it has a 'grade filter'.