The big issue is whether or not you have Agreed-Value coverage versus Market-Value or Replacement-Value coverage. If the former then you and your carrier have already come to an agreement as to the value of your car in terms of both a total loss or a portion thereof. If the latter then you and your carrier have agreed that the value of the car will be established at the time of the loss, regardless of what value may be stated in the policy.
Generally only Classic Car policies such as those offered by Hagerty, Grundy, Parish-Heackock, etc. have the Agreed-Value coverage and generally conventional policies such as those offered by State Farm, etc. use the Market-Value type.
What this means is that if someone steals your BJ8 and you are insured with Hagerty with a valuation of $50,000.00 you will only have to prove that the car was stolen and you owned the car at the time of the theft and you get your $50,000.00. With State Farm you need to show what the car's ACV (Actual Cash Value) was $50,000 and that would entail proving what you paid for it, what work you had done to it, what kind of shape it was in, whether the market on Healeys has gone down, etc.
If you need to drive your Healey to work, or if you don't own a regular car, or if you don't have a locked garage space that you can devote to your Healey or if you want absolutely no limitations on the way you can use your car then go get a conventional policy. If you can live with the conditions that various Classic insurers offer then pick the one with the best price, least restrictions, etc.