Carolyn -
If it's definite birth dates you want, then you have two choices. Either use the Camdex database, which is based on local records, as Ricky has suggested and has already given you the link for.
OR use FreeBMD to hook up the 16 children from the census returns to the registration quarters.
Using the 1881 - 1901 census returns provides names for all the children and gives them approximate birth years.
Now just look them up on Camdex or on FreeBMD. Camdex will give you a year, FreeBMD gives the quarter.
To get exact birth dates, you will need to buy their birth certs, either from Camdex or via the GRO certificate ordering service at
http://www.gro.gov.uk/gro/content/certificates/Not cheap! However, if you can be satisfied with a probable quarter of birth rather than an exact date, the FreeBMD data is good enough unless there is possibility of confusion - in which case you DO need the cert to sort out which one is "yours".
For instance, here are the three eldest children:
Births Sep 1875: CORNWELL George William Newmarket 3b 544
Births Mar 1877: Cornwell David Newmarket 3b 571
Births Jun 1878: Cornwell Alice Mary Newmarket 3b 579
There are no duplicate names, so the above are almost certainly the children you are seeking.
Between 1801-1837, the other site Ricky gave you will provide baptisms from the Cambs FHS database. There are 27 baptisms for Cornwells in Bottisham, and 67 in total for all variants of the name.
From the census returns, it looks as if George Cornwell b about 1853 who married Mary Ann Morley was the son of Isaac Cornwell b about 1817 and Rebecca.
Here's a likely marriage for Isaac and Rebecca from FreeBMD:
Marriages Jun 1839
CORNWELL Isaac Chesterton 14 69
PAPWORTH Rebekah Chesterton 14 69
The Cambs FSH baptism index will show you that Isaac was baptised in 1819 in Little Wilbraham (just a couple of miles from Bottisham) and was the son of James Cornell and Sarah of Little Wilbraham. There was another Isaac baptised in 1814, but searching the Cambs FHS burial database will show you that he died the same year.
With a name like Cornwell, you have to be alive to all manner of variations in the spelling of the name.
There are masses of online records - Cambs is covered better than many counties because of the Cambs FHS indexes of baptisms and burials 1801-1837, and the Camdex index to the LOCAL registers, although this is not yet complete. The Cambs marriage index is also not yet complete, and doesn't tie up brides and grooms, but is still a useful resource available for a small sum on CD from Cambs FHS.
But the trick is to be able to link up all the different resources to build your story. As I have suggested above, get the children from the census, find their birth registrations. The certificates will give you the names of their parents if you want confirmation of the census data. Then find the marriage certificate for the parents which will take you back another generation by providing father's names for bride and groom. And so on - untill you get back beyond 1837, or in the case of Cambs for baptisms/burials, 1801. Then you need parish records. If your village is covered, get the CD of the PRs from the FHS. My forbears are Isleham folk for generations - the CD of the Isleham parish records was a godsend.
No-one's going to have all the data on your family to hand to you on a plate - it actually does take quite a lot of work! And a bit of money too - I find a UK sub to Ancestry absolutely essential, and have invested vast amounts in GRO certificates. Luckily, FreeBMD is totally free, as it says, and FreeREG is slowly providing a similar service for parish records. The IGI database at
www.familysearch.com is free to use and is a wonderful source of information, although member contributed entries need taking with a large amount of salt.

If you just want to link up with other members of your family and share their data rather than doing the nitty gritty yourself, why not try Genes Reunited? A quick search shows an Isaac and a George of the correct ages in other people's trees. Might be worth a try?
Personally I prefer to do my own digging about and make my own links. Genes Reunited can often be the lowest common denominator, with many people making all the same errors....
Good hunting....