This had a lot of coverage on the local news yesterday, and BBC South are planning another item tonight.
As far as I can tell, the reality is not as dramatic as the headlines suggest. The Pre-War Austin 7 Club, which has held its national rally at Beaulieu for 60 years, sent an email last night with this response from Beaulieu:
"We would like to reassure you that firstly this isn't an immediate change, and that secondly Beaulieu intends to continue being a leading visitor attraction on the south coast and operate a motor museum as part of the visitor experience, as it has done for over 70 years. Beaulieu’s motoring events will be unaffected, with no change to our events calendar and we look forward to welcoming visitors to the much-anticipated International Autojumble in September."
The bottom line seems to be that the National Motor Museum trust will find a new home but Beaulieu will carry on as now. A lot of the cars currently in the museum belong to Beaulieu anyway, perhaps they'll rename themselves "The Montagu Motor Museum" as before.