Lord Lloyd-Webber is preparing for a production of Cinderella, which is scheduled to open for previews on June 25 ahead of its world premiere in July.
But the June 21 “freedom day” is in doubt due to concerns over the impact of Covid-19 variants.
“We are going to open, come hell or high water,” Lord Lloyd-Webber told the Telegraph.
Asked what he would do if the Government postponed lifting lockdown, he said: “We will say: ‘come to the theatre and arrest us’.”
Speaking on Wednesday morning, the composer and theatre boss urged the Government to publish information from pilot events conducted over the last few months.
He told Radio 4’s Today programme that “having spoken to leading counsel on this, that the feeling is that the reaction of the Government, if they do stop us from going forward, is neither rational, nor is it proportionate”.
He added: “I believe that this is the Government’s moment to show that they really do care about the musicians and the actors and all who work in live events.”
Under current Government guidance, social distancing in bars and restaurants is in place, with limits on audiences in theatres and cinemas also being implemented.
Speaking on Sky News, Communities Secretary Robert Jenrick said he “completely sympathised” when asked about the composer saying he would risk arrest in order to fully reopen his theatres.
“We want to get them open, we are doing pilots, we want to get those theatres open so great new productions like Cinderella can open,” Mr Jenrick told presenter Kay Burley.
“I know that people are desperate to go to them, tickets are selling fast for all those productions because people have been away too long.
“But you have just got a few more days to wait until the judgment that the Prime Minister is going to make on the basis of the data.”
When asked if Lord Lloyd-Webber should be arrested if he does open theatres without restrictions relaxing, Mr Jenrick said: “We all have to abide by the rules.
“I’m not going to get into speculation about that but we want to get those theatres back open, obviously as quickly as we can, and to support people like Andrew Lloyd Webber so that we can all enjoy brilliant productions in the West End once again.”
Digital, Culture, Media and Sport Committee chairman Julian Knight sympathised with Lord Lloyd-Webber, saying: “It is very frustrating for the live events industry as we can see from Lord Lloyd-Webber’s comments, though clearly I wouldn’t support anyone breaking the law.
“With the June 21 reopening on a knife-edge, the Government needs to be absolutely upfront about the results of its pilot events and how they feed in to decision-making.”
This is not the first time Lord Lloyd-Webber, 73, has criticised those calling for a delay in reopening.
Last week he told the Daily Mail he may take legal action if his theatres are not allowed to welcome back crowds at full capacity.