Nobody in the UK "pays" for the royal family.
"Over time, more and more income from Crown lands was handed over to government, and as such the Sovereign was directly responsible for less and less government expense.
The profits of the Crown Estate are public money and all go to the Treasury. This is then collected together with the income the Treasury gets from general taxation and other sources, into one pot: the “Consolidated Fund”. We’ll refer to this pot as “public money”; most of it comes from general taxation, but some of it is from non-tax sources (such as the Crown Estate profits).
The Treasury then pays the Sovereign Grant to the Queen, which is currently calculated as the equivalent of 25% of the Crown Estate’s profits two years previously. The amount of the grant isn’t determined by how much the royal family plans to spend." (source: Full Fact)
According to Wiki, "Historically, Crown Estate properties were administered by the reigning monarch to help fund the business of governing the country. However, in 1760, George III surrendered control over the Estate's revenues to the Treasury,[5] thus relieving him of the responsibility of paying for the costs of the civil service, defence costs, the national debt, and his own personal debts. In return, he received an annual grant known as the Civil List. By tradition, each subsequent monarch agreed to this arrangement upon his or her accession. However, from 1 April 2012, under the terms of the Sovereign Grant Act 2011 (SSG), the Civil List was abolished and the monarch was thenceforth provided with a stable source of revenue indexed to a percentage of the Crown Estate's annual net revenue (currently set at 25%).[16] This was intended to provide a long-term solution and remove the politically sensitive issue of Parliament having to debate the Civil List allowance every ten years. Subsequently, the Sovereign Grant Act allows for all future monarchs to simply extend these provisions for their reigns by Order in Council.[3] The act does not imply any legal change in the nature of the estate's ownership, but is simply a benchmark by which the sovereign grant is set as a grant by Parliament."
So the contract handing over the profits of the Crown Estate need to be renewed upon the accession of each monarch. If Charles decides to not do this (won't happen, but just what ifs), he can because it goes back to his ownership.