CAO 48.0 para 1.3 states that the holder of a CPL or ATPL who is engaged in commercial operations must include all private flying when calculating flight and duty limitations.
I take this to mean if you only fly privately on a commercial licence flight and duty is not an issue. But as soon as you conduct a commercial flight al flight time regardless of its nature must be included in flight and duty calculations.
One of the early CAA dispensations to CAO 48 did allow private flying to be kept separate to commercial flying, but the dispensations is not now available.