The Goodwood Festival of Speed falls in July each year - the weekend is selected to allow the F1 drivers and teams to participate (as much as their sponsors allow). There is a competitive element on the speed hillclimb but for the most part it is a great show.
These dates for the FoS fall between the IoM TT and Manx weeks. There is a museum on the IoM which includes vehicles (I have not visited).
Nothing to do with motorbikes - the water speed records week on Coniston Water is at the end of October, in 2019 the dates are likely to be 28th October to 1st November.
As for the Museums, the two key ones are indeed the National Motorcycle Museum on the edge of Birmingham and the National Motor Museum, Beaulieu (South of Southampton). Then the list grows depending upon interests and how much you want to see in one place. The fastest car in the world is in the transport museum Coventry, the motor vehicle centre of the UK, and a short drive to Triumph in Hinckley. BABS is often in the Pendine Museum of Speed in the summer, Pendine is in South Wales. Donington Park in the East Midlands houses the best F1 car collection anywhere and is a 'stones throw' from Norton. Cumbria and the Lake District is 'focal' for many locations of Campbell (Malcolm and Donald) memorabilia (Lakeland MM already mentioned and Ruskin Museum in Coniston). [The Capital, London houses the main Science and Arts Museums but there are other locations too].