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John Barber took out a number of patents, most memorably for a gas turbine in 1791.
One source states that he was born on 22 October 1734 at Greasley, Notts, the son of Francis Barber (coalmaster) and Elizabeth Fletcher. Went bankrupt c.1784 and moved from Stainsby House, evidently to Attleborough, Nuneaton, where he died on 6 November 1801. Obtained his first patent in 1766. His patents of 1773 and 1792 concerned smelting, while another in 1776 related to an impulse steam turbine. His best known patent, of 1791, involved a gas turbine.
Although his patents are well-documented, there is some uncertainty about biographical information. One contemporary report, which credibly relates to the inventor, gives his date of death as 1793, not 1801:-
1793 'Lately died at Attleborough, John Barber, Esq; formerly or Hansby-House [?Stainsby House], in Derbyshire. He was a man of universal knowledge. In his death the world has lost a sound philosopher, an eminent mineralist, and a great mechanic ; and who expended an ample fortune in benefiting mankind. His decease is greatly lamented by the indigent in general, as he was upon every occasion a liberal benefactor. His remains were interred at Monyash, near Buxton, in the family vault of the Goodwins, of that place, into whose family he intermarried.' 
Given the references to two different dates of death, we must recognise the possibility that there was another John Barber, concurrently engaged in similar activities in the English East Midlands. Investigation is made difficult by the broad extent of Barber's business and property interests, and his changes of location. The following references have sufficient common factors to give confidence that they relate to the same John Barber, inventor and mine owner, and that he died in 1793, not 1801.
One source identifies John Thomas Barber Beaumont, English coalmaster and inventor, and states that he was born in Nottinghamshire, but moved to Warwickshire in the 1760s to manage collieries in the Nuneaton area. For a time he lived in Camp Hill House, and later lived in Attleborough. He patented several inventions between 1766 and 1792, of which the most remarkable was one for a gas turbine. Barber was the first person to describe in detail the principle of the gas turbine, and in recent years a working model based on Barber's specification has been built. The source gives his date of death as 6 November 1801
Memorial inscription: 'John BARBER, Esq, formerly Stansby House, County of Derby, married Martha eldest daughter of George GOODWIN, of Moneyash, Gent
Died 17 June 1793, 58
His widow, tenderly respected the memory of a beloved husband has caused this monument to be erected.' 
1771 Articles of purchase made between John Barber of Stainsby and Richard Lowe of Locko Park for Heanor and Langley Colliery, Derbyshire, 31 December 1771 
In 1776 Johann Jacob Ferber, German mineralogist, toured Derbyshire. He observed two steam engines at Stainsby and Simonfield, One was the invention of Mr Barber the proprietor of the mine, which differed a little from the 'ordinary' engine. 'John Barber became bankrupt in 1784 and the whole of his Smalley estate was placed on the market. Also owning property in Nuneaton, Warwickshire he moved away from Derbyshire. Stainsby House was purchased by the Sitwell family.'
1782 'On Thursday died, at his House in the Friar Gate, in a very advanced Age, Mr. Barber, Father of John Barber, Esq formerly of Stansby in this County. 
1783 Reference to 'Dividend Payment' by 'John Barber, of Wedington the County of Warwick, Miner, Dealer in Coals, Dealer and Chapman; at Guildhall, London.'
1789 Advertisement for the sale by auction of 'A VERY VALUABLE FREEHOLD ESTATE belonging to John Barber, Esq; and situate at Smalley....' The property included land, buildings, 'A new overshot Water Corn-Mill, with three Pair of Stones, and Dresing-Mill, together with a Mill Dam and Damstead', a 'one fifth Part of the Manor or Royalty of Smalley, Morley, and Kiddersley. .... The Coal, Iron-Stone, and other Minerals, within the above-mentioned Lands, and the Wastes and Commons belonging to the said Manor, are not included in the above mentioned Lots.' For Particulars apply to ABRAHAM BRACEBRIDGE, Jun. Esq; Atherstone; JOHN BARBER, Esq; Drayton-Hall, or to Mr. OWEN, Attorney, in Atherstone.
1789 Advertisement concerning Haunch-Wood Colliery near Nuneaton, advertising the sale of leasehold rights and interests of John Barber of and in coal mines at Nuneaton and Chilvers Coton. On the premises were a 'good new steam engine' with a cylinder of 4 ft bore and 9 ft stroke. Apply to John Barber at Drayton, Leics., or Mr Owen, Attorney, at Atherstone 
1790 'Mr. JOHN BARBER'S BANKRUPTCY. ALL Perfons having any Claims or Demands upon the Estate and Effects of Mr. JOHN BARBER, late of Weddington, in the County of Warwick, but now of Drayton, in the County of Leicester, Miner and Coal-Dealer, are desired to send a Particular thereof to Mr. OWEN, Attorney in Atherstone, on or before the first Day of May next, in order that the same may be finally adjusted and settled. Atherstone, March 20th, 1790.' 
1790 Advertisement: 'WANTED, at Nuneaton Colliery, One Thousand Feet of good ASH or ELM TIMBER, sawed into Scantlings of four Inches square, and delivered at the Colliery Wharf, near Nuneaton, 11 Miles from Coventry. Any Person willing to contract for delivering the same in a given Time, and to be paid for upon Delivery, may be treated with, applying to Mr. John Barber, at Attleborough, near Nuneaton, Warwickshire, either personally or by Letter. N. B. A large Quantity of good OAK. POSTS, six Feet long, are also wanted.'
1817 Regarding Stanesby or Stainsby House: Sold to John Fletcher in 1712. In 1783 it was 'purchased of the assignees of his nephew and devisee, John Barber by Samuel Buxton....'
1905: Regarding Stainsby: 'It afterwards became the property of the Fletchers, who were colliery owners in the neighbourhood. From them it passed to the Barbers, as appears from a mural monument to the Fletchers in Horsley Church. John Barber, living at Stainsby in 1767, was the son of Francis Barber, Esq., of Gresley, by Elizabeth, sister of Robert Fletcher, of Stainsby, who died in 1731, and the daughter of Robert Fletcher, of Kilbourne, who died in 1711.
1792 'A method of smelting and purifying Fossil-Coal, Iron-Stone, Iron-Ore &c., by Steam, Air and Fire, and impregnating the same with inflammable air, thereby producing a tough metal. Dated Dec 22, 1792' 
An authoritative account of the machine, as described in Barber's Patent (English Patent 1,833, 31 October 1791), is given by Lyle Cummins. This includes a drawing from Barber's Patent. The equipment included two retorts for making gas from coal. The gas was burned as it was produced, and passed though a nozzle to impinge on an impulse-type turbine. Before combustion, the air and gas were compressed by a piston-type compressor driven from the turbine via gearing. Provision was made for injecting water into the burning gases 'to prevent the inward pipes and mouth of the exploder from melting by the intenseness of the issuing flame.' The patent also suggested application of a jet of hot gas to propulsion of a boat (jet reaction).
The overall concept is quite remarkable, given the early date, and noting the limited experience of coal gas production at the time.