http://www.englishheathenism.homestead.com has some information on Saxon religion.
Birmingham wasn't really settled until the 6th century so the local Saxons are likely to have been Christianised.
As has been mentioned, Wednesbury is named after Woden, and there is a statue of Sleipneir in Wolverhampton.
"Midlands" covers a very large area though. From Shropshire down to Oxford! The Thames is called Isis along part of its course.
A book which gives a starting point is "The Isle of Many Gods" by Sorita and David Ranking. It doesn't give a great deal of information about each God, but does give enough information to make a start on deeper research.
Britain is a nation of immigrants, so many of the tribes and immigrants have brought their own Gods with them. I'm fairly certain you could pick any God and at some point someone in the Midlands will have honoured them.
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Rhiannon