Although first mooted in the 1840s, the Lynn & Fakenham Railway was not opened, over its full length, until 1880. It only had a short independent life, being absorbed into the Eastern & Midlands Railway in 1883.
A look at the history of the line and it’s route through the Norfolk countryside is for a future post.
The Lynn & Fakenham Railway is mentioned in an article in the journal “Railway Archive.” Interestingly, that article is about the locomotives which were initially purchased for the Cornwall Minerals Railway. 
The Cornwall Minerals Railway developed out of a series of older Tramroad which served the Cornish Mining Industry. It owned and operated a network of 45 miles (72 km) of standard standard gauge railway lines in central Cornwall. It started by taking over an obsolescent horse-operated tramway in 1862, and it improved and extended it, connecting Newquay and Par Harbours and Fowey.
It had a chequered history having been hurt by a collapse in mineral extraction due to a slump in prices. But after a period in bankruptcy it recovered enough to take over a defunct route between Fowey and Lostwithiel – the Lostwithiel and Fowey line.
In 1896 it finally sold its line to the Great Western Railway which had been leasing it for some time.
Its main passenger line from Par to Newquay is still in use as the Atlantic Coast Line, and also carries some mineral traffic, but the Par to Fowey line has been converted to a private road. The Cornwall Minerals Railway was adventurous in its intentions and purchases. It anticipated far more traffic from the mines than was to materialise and bought 18 (yes, eighteen) 0-6-0T steam engines to serve the anticipated high demand.  When the line was leased to the GWR in 1877, the new lease-holders quickly realised that the over provision of motive power was a financial drain on the Line. The GWR returned 9 of the engines to their makers, leaving 9 to serve the needs of the Line. [1:p30]
Of the 9 remains locos, a further one was sold by 1883 to the Sharpness New Docks Company and based on the opposite side of the River Severn from the Forest of Dean. [1:p31]
We are interested, in this article, in the fate of the 9 locos returned to Sharp, Stewart. Or, at least, 8 of those 9 locomotives. 8 were purchased by the Lynn & Fakenham Railway and ended their days in various guises on the Midland & Great Northern Joint Railway (M&GNJR) which was the ultimate successor to the Lynn & Fakenham Railway. [1:p30] A first batch of three were sold to the Lynn & Fakenham in 1880, a further five were sent to the Lynn & Fakenham in 1881. [1: p36]
Incidentally, the last of the 9 locos returned to Sharp, Stewart was sold to the Colne Valley & Halstead Railway before ending up at a colliery in Northumberland. [1: p30]
Treloar comments that the Lynn & Fakenham’s successor, the M&GNJR was “despite their lack of success … inspired … to design and build a later type of 0-6-0 tank with similarities to the original locomotives, some of them even using the wheels from the ex-CMR engines.” [1: p30]
This is recognised at least in part by the LNER Encyclopedia which says:
The Lynn & Fakenham Railway and it’s successors clearly had problems with the original CMR locomotives. They did not last long in their original guise. The lack of coal space was a major problem! By the time they were in use on the M&GNJR, they had been provided with tenders, as shown above. The tenders were all fabricated by Sharp, Stewart in the 1880s to their standard 4-wheel design. A series of pictures is provided with the article in Railway Archive. [1: p36-39]
“The Midland & Great Northern Joint Railway’s (M&GNJR) ‘Shunting’ Class (LNER J93) were designed by Marriott and built at the M&GN’s Melton Constable’s works. In common with many M&GN types, the Shunting Class followed Midland Railway practice and included a number of Derby design features, such as the cab, tanks, and boiler mountings. The boiler drawing was made at Derby in 1896, and the nine locomotives were built at Melton Constable between 1897 and 1905.
Most of the J93s were built carrying the ‘Rebuilt Melton Constable’ plates, and six of the class (Nos. 93-8) were reputed to have been rebuilt from locomotives that had started out on the Cornwall Minerals Railway (CMR). These were built by Sharp, Stewart & Co. in 1874, and acquired by the Lynn & Fakenham Railway in 1880-1. These were then inherited by the Eastern & Midlands Railway – predecessor of the M&GN. The stock register describes the J93s as new locomotives, and Mr G.B. Clarke (draughtsman to Marriott) is on record as emphatically stating that the J93s were new locomotives. Therefore, J93s Nos. 93-8 should really be considered replacements for the ex-CMR engines. After saying this, there is some evidence that some of the J93s carried ex-CMR wheels at one time or another. These had ten spokes and built-up balance weights, whilst the new wheels had twelve spokes and cast-in crescent weights. Some photographs from the 1940s show individual J93s carrying a mixture of both wheel types!” 
In addition to these 0-6-0 locomotives, the Lynn and Fakenham bequeathed a number of other engines to the Eastern and Midland Railway. These included:
Seven 4-4-0T locomotives built by Hudswell Clarke for the Lbetween 1878 and 1881; 
Four Beyer Peacock 4-4-0 locomotives built 1882/1883. These were the first of a total of fifteen of the class. The remaining eleven were built for the Eastern and Midlands Railway before 1888. 
1. Peter Treloar; A Scattered Family: The Cornwall Minerals Railway’s 0-6-0Ts; Railway Archive Issue 30, Black Dwarf Lightmoor Press, 2011, p27-40.
2. https://en.m.wikipedia.org/wiki/Cornwall_Minerals_Railway, accessed on 16th November 2019.
3. https://www.lner.info/locos/J/j93.php, accessed on 16th November 2019.
4. https://www.rmweb.co.uk/community/index.php?/topic/131449-creating-a-believable-freelance-pre-group-company, accessed on 16th November 2019. The provenance of the photograph is unclear. It appears on ‘rmweb’ as part of a long discussion about creating a realistic pre-grouping model railway.
5. https://en.m.wikipedia.org/wiki/Eastern_and_Midlands_Railway, accessed on 16th November 2019.
7. https://www.lner.info/locos/D/mgn_arebuild.php, accessed on 16th November 2019.