There’s always the Cotswolds Motoring Museum in Bourton-on-the-Water.
Bourton is also a great place to spend some time, and the Cotswolds is a great area for touring with many other places to visit and loads of places to stay.
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Fleet air arm museum is superb and don’t forget the tank museum which is within reach. I’ve done motor museums and love them but I get a lot more out of air and tank museums I’m afraid 
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Imperial War Museum DUXFORD - Especially on days where there are flying demos.
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I remember going to Bovington tank museum years ago and getting travel sick on the simulator!
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Still happening nowadays to soldiers in the Ajax armoured vehicle apparently!
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We had a day out to the Haynes Motor Museum back in 2006. If I remember rightly I had to be dragged out…
. Same thing happened again in the Railway Museum in York 
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I always enjoy a visit to the National Railway Museum in York. We are only 40 minutes drive away. Some of the archive films they show up on the mezzanine are terrific. I love watching things being made. Just to whet your appetite, a link to a film which shows the building of a steam locomotive from the beginning. Note the complete lack of eye and hand protection and workers wearing jackets, collar & tie!
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I went there last year, it’s been changed somewhat from the last time I visited. Aware of the changes over the last couple of years, been many times, yes it’s free but I think it’s not as good as it used to be. Also, the roadworks around there made it a long trek just to get in, a few enthusiasts I spoke to were also bemused by the changes.
Loved the video - I had a tour of Crew Loco (where this is filmed) back in the late 1980s when they were building the Class 91s and my guide (my boss at the time) commented upon entering the main assembly shop how much hearing loss compensation had been paid out for work undertaken in there. Very very loud, so the lack of hearing protection really jumps out. Plus at that time lots of asbestos. Not to mention all the fumes… Loved ‘Mr Hammer’ at the 4.30 minute mark:)
Back on track - Newark Air Museum is a fun visit and not too far from you (as OP) if you’re in East Yorkshire. Just Jane at Lincolnshire Aviation Heritage Centre, in East Kirkby, likewise - the exhibition of crashed aircraft parts recovered locally is worth the visit alone.