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Despite having no railway, Kirkleatham does have a row of railway cottages from 1847, they were dismantled and moved from Redcar in 1861 when the railway line was extended to Saltburn.
Designed by John Middleton, these are the last remaining buildings of the Middlesbrough & Redcar Railway.
Was the railway line realigned around the Coatham (?) area when it was extended to Saltburn? An investigation using Google Earth seems to show earthworks of a trackbed nature in this area.
You can see the original path here :-
http://www.geocities.com/waggonways/nz/55/nz5520.html
Are you sure you are not talking about the realignment that was carried out in the early 1970′s which saw the end of Warrenby Halt (‘teacake halt’ as it was known) and the opening of the new British Steel Redcar station. This pulled the track about 1/2 mile soutwards from the old route
Indeed there have been two changes, the most recent in the 70s as mentioned by David.
The earlier one was as follows :-
The original 1846 station was sold and became the Central Hall.
The railway land was developed into the Queen Street area.
I have added a map which shows the two locations, and the railway terrace is marked too