Hi Richard....
Hopefully things will become clearer once you get the birth certificate.
I looked for a birth for you in Nottinghamshire for Charles - there are 89 Pole christenings; only one Charles & that was for a Charles Robert Pole, 1828.
One thing I did notice..... and may be a red herring....
The marriage that Mike has given you for Charles Pole & Elizabeth Eames, has one of the witnesses as John Billington and on the 12th July 1824 at Nottingham St Mary there is a marriage for a Thomas Billington to a Sarah Pole.
I have been lurking in the Newspaper's again!.... even they show some discrepancies to the information you have....with the couple both dying in 1884, the newspaper and FreeBMD having her as Eliza.
Have you seen the Will listed on Ancestry for Charles & Eliza 1884? on the entry for Charles it says proved at Leicester by John Pole of 317, Humberstone Rd, Leicester in said county, the son one of the executors.....
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The Leicester Chronicle: or, Commercial and Agricultural Advertiser (Leicester) Saturday, June 15, 1844
Deaths
On Sunday, aged 46, Eliza, wife of Mr Charles Pole, Carpenter, Friar Lane.
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Leicester Chronicle and the Leicestershire Mercury (Leicester), Saturday, May 24, 1884
Deaths
Pole - On the 20th ult, ELIZA, wife of Charles Pole, 51 Claremont Street, Belgrave, aged 68.
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Leicester Chronicle and the Leicestershire Mercury (Leicester), Saturday, October 25, 1884
Deaths
Pole - On the 13th inst, at his residence, 51, Claremont Street, Belgrave, Mr Charles Pole, superannuated officer of the County Police, aged 74.
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Kind Regards
Sheila.