Hi J.H.
I have no personal experience of the Beverley and Yorkshire area in general, but I would think that the same ideas apply country-wide.
While there may be no certificates pre-1837, hatches, matches and dispatches were still recorded in the parish registers and that is where you need to search next. Some may be available online - no idea. Try entering "parish register Beverley" into Google and see what comes up. Older people in the census, particularly 1851, can also help provide another starting point to look for baptisms etc.
The IGI is always a good starting point as you say, but there comes a time when you need more concrete information. Some parish registers may be very descriptive in their burial records and even the most humble parishioner will be given an age and some description. Some if not most will not. But they must all be buried somewhere, even without a headstone. You could ask for look-ups in the National Burial Index or search for burial records online. Familyhistoryonline (a pay per view site) may also be albe to help you out here. And even humble parishioners can sometimes leave a will - definitely look for those.
Also check the a2a website:
http://www.a2a.org/uk/for your ancestors name or abode. You would be amazed what sometimes crops up.
Names which are used regularly are often a sign of all the same family. Then there are settlement certificates/removal orders or other poor law records, if your ancestors happen to fall into that category. Other parish chest records as well. The list is potentially endless. Even humble folk leave some trace behind them. Whatever you do, don't give up - serendipity is a wonderful thing.
Good luck
Nell