Customer is probably making the common confusion that building control and planning are the same thing. Planning is "what is built and where", building control is "how it is built".
Planning is needed in fewer instances than BC, as some rights to develop a property are permitted by law rather than by considered application. An LDC is confirmation from the council that a proposed development is permitted by law and needs no planning decision from the council. If the customer wants one then following woody's advice is prudent - if you're going to contribute to the council Christmas meal fund, you might as well do it before just to be sure your scheme actually follows the law and is permitted. It'd be a nuisance to build a dormer that falls foul on some small point, and have to rip a chunk of it out again upon purchasing an LDC post rather than prior.
FMT mentions plans, and theyre a good idea not only for getting paperwork out of planning and building control, but for establishing a contract with the builder to ensure what is wanted, is actually what is delivered. You sure can get away without plans, trust the builder knows the rules, builds a legal dormer and gets it signed off by Bc under the building notice rather than full plans route, but it's far riskier than getting proper plans drawn, approved, costed and delivered. Few builders would want to quote a full and final price based on a 15 minute chat of "I want a dormer from here... To here.."