This basically means that if the cost of the materials in a job exceeds 2/3 of the VAT excl price to the customer then the standard 21% rate will apply and not the reduced 13.5% rate. It's to stop a situation where, say, you have a repair job replacing a burner on a heating system. The burner costs 200+VAT. The labour charge is say 50 + VAT, if you apply 13.5% to the total in that case, the person billing the work gets back more VAT than they pay.
You need to take (a) the cost of materials, add (b) the labour charge and see if (a) / (a)+(b) > 66.67%. In the above example 200/(200+50) = 80% which > 66.67% so in that case the job should be charged at 250+21% VAT.
From
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17.4 The rate of VAT applying to services, including building services, depends on the “two-thirds" rule. This provides that a transaction is liable to VAT as a sale of goods at the appropriate rate and not as a service, if the value of the goods used in providing the service, that is their cost excluding VAT to the service contractor, exceeds two-thirds of the total VAT exclusive charge to the customer.
The “two-thirds" rule does not usually affect building services in which the labour element is substantial. It would be likely to come into operation in the case of a service consisting of the supply and installation of, say, a transformer or a strong room. The possibility of its application should never be overlooked and contractors should consult the local inspector of taxes if there is any doubt about the correct liability to tax. Sub-contractors, in particular, may find that the 21% rate may apply to their portion of a main contract even though the main contract may itself be liable at the 13.5% rate.