Yes, the first Lord Newborough must have had a strong inclination to preserve his lineage as his only son (Hon. John Wynn, b. 1772 - d. 1800) from his first marriage (m. 15 Sept. 1766, Lady Catherine Percival, d 2nd Earl of Egmont) predeceased him by seven years. He then married secondly Maria Stella Wynn (aged 13 at the time) and had two further sons (both the 2nd and eventual 3rd Barons Newborough).
Without the time for a deep dive, it appears that an interesting mystery surrounds the ancestry of his second wife. She claimed throughout her life that she was descended from French royalty, but this was questioned even during her lifetime. She apparently was somewhat of a scandal even then.
As far as the original post goes, I believe the first peer to inherit in the 18th century was the Scottish peer John Kennedy, 10th Lord Kennedy and 8th Earl of Cassilis. He was born in April 1700 and inherited upon the death of his grandfather the 7th Earl on 23 July, 1701.