Is there a freely available index of construction labour prices?

We are a small specialist subcontractor, and a contractor has asked us to price a package of work that will run until mid-2024. We will require that a fluctuations clause is included in the subcontract, although we don’t know the detail of the subcontract yet.

The main cost centres in our proposal are aluminium materials, and labour for installation. We want to reference the fluctuations clause against indices for these specific inputs. For aluminium, we can easily obtain and reference an LME index. Is there any similar index for the costs of skilled and unskilled labour on construction sites?

I am aware that RICS offer a service called BCIS but this has to be paid for, and we’re hoping to find something freely available, so that future adjustments don’t depend on a current subscription.

I have looked at what ONS can offer, but they don’t appear to split out the labour element specifically.