Hello Herb,
I have visited the JDHT museum at the factory, and also the Coventry Motor Museum in the center of town, but can't say I'm familiar with a Jaguar Museum in the city.
When the Factory was open, the JDHT Museum was open on the Last Sunday of each month, but I have no idea if it is anymore now that the factory has been sold. Truly a wonderful collection. I have pictures and an article here:
https://www.jag-lovers.org/saloons/mk1_50/
The Coventry motor Museum as well was well worth the trip. As Coventry was the center of Automobile manufacturing during the the 20th century, many examples of britains finest automobiles are represented. You might also like the Thrust exhibit - The world land speed record car is there as well.
Dan Davis 1959 3.4 Litre (Mark 1) RHD Santa Monica, CA