Yes, we do have a little information on a Thomas Berrington of Leicester. Thomas Berrington m. Ann Coulson at St Margaret's Leicester, 26/4/1764. In 1789 he was a grocer, in 1794 we believe he was an aucioneer. They had a son Thomas, b. 1/4/1772, chr. 26/4/1772 and buried at St Margarets, July 1850. We have no record of his marriage but he was buried in July 1850. Thomas and Ann Coulson also had a son John Berrington, who was appreniced to a cutler and later became an optician. He was chr. 3/2/1765. His first wife was Mary but we have no record of her surname or of their marriage, They had a son called Thomas who was born 4/8/1797 and chr. at At Margaret's Leicester 14/8/1797. He married Mary Lansbury (surname unknown). In the 1871 census, he was living in Harrow and he died in the Sept qtr of 1872.
I hope this helps. Incedentally, we can trace the family back to Hathern, Leics. in about 1550