These are both County Deputy Lieutenant’s silver plated buttons. (Victorian crown in wreath). The first at 22mm, second at 20mm.

From the contemporary directories and press:

1823 Kent’s London Directory: Smith & Trimnil, gold lace Manuf. 12 Piccadilly.
1843 Post Office London Directory: Smith Charles, Gold laceman &c. 12, Piccadilly.

London Gazette 3 April 1868:
NOTICE is hereby given, that the Partnership heretofore subsisting between us the undersigned, Charles Smith, John Godwin Smith, and Edward Howard Markes Smith, carrying on business together as Gold Lacemakers and Army Accoutrement Makers, at No. 12, Piccadilly, in the county of Middlesex, was this day by mutual consent dissolved, as from the 1st day of January, 1868. All debts due to and owing from the said partnership will be received and paid by the said John Godwin Smith, by whom the business will in future be carried on.—As witnessed our hands this 17th day of February, 1868
Chas. Smith.
John Godwin Smith.
Edward Howard M. Smith

Globe 17 October 1888
London Bankruptcy Court:
Yesterday, at the London Bankruptcy Court, a meeting was held before Mr. Registrar Linklater, for the public examination of John Godwin Smith, described as of New Burlington Street and Old Burlington-mews, and Tunbridge Wells, gold lacemen and accoutrement makers, trading as “C. Smith and Son” and “J. Wright and Co.” The receiving order was made on August 1, and the statement of affairs shows total liabilities £68,689 14s. 3d., of which £42,331 13s 3d is expected to rank, and assets of £7,244 2s. 2d. In course of examination the debtor stated that on retirement of his father, in 1868, he took over the business and undertook to pay his father an annual sum of about £800, to cover interest on estimated surplus in the business, and in consideration of the transfer. He had no capital of his own to commence with, but in 1869 introduced about £2,000. He had carried on the business by borrowing large sums of money. In 1878 he assumed that he was in a solvent condition. He attributed his failure to heavy interest on borrowed moneys, and other causes. In course of further examination the debtor explained that the business had been sold, and the purchaser was now carrying it on. He (the debtor) had no interest whatever in it.

London Gazette 20 June 1890 – High Court of Justice in Bankruptcy notice:
Director: Smith, John Godwin (trading as C. Smith and Son, and as J. Wright and Co.)
Address: 5. New Burlington-street and 5 and 6, Old Burlington-mews, both in Middlesex, and Baston Cottage, Tunbridge Wells, and Muxlewell Farm, Pembery, both in Kent
Description: Gold Laceman and Accoutrement Manufacturer.

1891 Post Office London Commercial and Professional Directory: Smith C. & Son, gold lacemen, military embroiderers, army contractors, sword cutlers & army accoutrement makers, 5 New Burlington Street W.