Hello Mr Dudley
I think that the answer to this one is lost in the mists of time, but thought that I would reply as I too descend from the marriage of Bernard Cotton and Rebecca Halford. I have an 1860 letter addressed to my great grandmother, then Miss Sarah Harrison, which details her descent from the Cotton/Halford families via her grandfather, Thomas Chapman Harrison who married Elizabeth Fowke(s). This descent is detailed in Nichols and the Harrisons, being yeoman farmers and nurserymen of Leicester made good, were obviously seeking to 'beef up' their family tree at that time. Another member of the family had a parchment pedigree of the Cotton and Halford families drawn up from Nichols in the late 19th century, and I have a photocopy of this.
Having investigated this link years ago when I researched it in the Leicester Record Office, I have to say that I was a little dubious as I wondered why Eleanor (various spellings) Cotton, daughter of Bernard Cotton and Rebecca Halford presumably gentry, was marrying Robert Paul(l), a framework knitter who couldn't sign his name on the marriage license. You do however mention that Bernard Cotton was apprenticed to a trade himself and I wonder what that was? I have recently gone through everything again on Find My Past and am a little happier with the link, especially as it is evident from his will that Robert Paul was a man of property and he had learnt to sign his name by the time of his death. I am not too worried by the few anomalies of date such as Eleanor's baptism (the correct date seems to be March 10th 1700 at Dadlington) and Bernard Cotton's burial (March 25th 1733 at Wistow). The different date on the stone slab for Bernard Cotton is confusing, but sometimes memorials were laid down many years after the event, and this could be an explanation.
It is frustrating that Bernard Cotton doesn't show up in more documents and that there aren't relevant Halford Wills for that time, but perhaps, considering the dates, we are lucky with what we have got.
Best wishes
John