Not a firm of Dickensian solicitors, but three unique rhymes.
List of words claimed not to rhyme with any other English word often include silver, bulb and purple, but these do have rhymes, and although (obscure and possible obsolete) they are in the Oxford English Dictionary.
Silver rhymes with Chilver, a young female lamb.
Bulb rhymes with Culb, the item of alchemistic glassware on the bench to the left in this picture from the Welcome Collection¶. AKA a retort.
Purple rhymes with hirple. a Scot dialect word meaning to walk with a pronounced limp.
I found these words when searching for unique rhymes—pairs of words that rhyme only with each other, and with no other word. So we can say for example that the only word that rhymes with silver is chilver and vice versa (although verifying this with certainty would be challenging—what dictionaries do you consult, what counts as a rhyme, how do you even search in a language where urp cam rhyme with irp and erp and earp (as in Wyatt)?)
¶ Woodcut of alchemist trying to transmute metals, circa 1503. Wellcome L0012391