You could try BR Database (type that into Google).
Thank you guys, the link is useful - intrigued as to why the data seems to stop around the end of 1988. Interesting that there are no 37/4 entries (for example 37289/37408 was at Eastfield from 1985 onwards and does not appear).... this is a fantastic allocation database and although there is some missing info it should go a long way to help you find what you need:
http://www.brdatabase.info/sites.php?page=depots&subpage=locos&id=192
True Richard, www.12csv.com is a very good source of info which is accessible by engine number so not so useful given that my enquiry is driven by depot.There are a couple of websites with detailed records of class 37s such as the class37 loco group. But the info is by loco so you need to have an idea which loco it might have been. Is it going to be a 37/4 as they are easy to check. Or you could buy a 1989 platform 5 loco book.
Thank you, an Eastfield loco in Petroleum Sector circa 1989... looking promising.37184 appears to fit the bill http://PaulBartlett.zenfolio.com/brclass37/e6bfefa2 - newly repainted when seen in August 1989.
37184 appears to fit the bill ...
Whilst my initial enthusiasm was sated by Paul's suggestion of 37184 this engine did not tick all of the boxes as Peter wished for a split headcode box engine. I decided to follow Richard's suggestion and explore some of the Class 37 websites which provide allocation and liveries by engine number... quite a mind numbing task when the haystack is big and the needle is small. Out of the blue I received a suggestion that I look at 37 359.... 37035 was a petroleum sector loco but in blue large logo livery, other than 37191 also in large log, all other ED petroleum SS locos are shown as in blue in 1989.