How much deposit can I pay

10% of the total labour cost is decent! That Should be more than enough.

It is not normal practice to pay for building work upfront, the argument of paying for materials is a non starter, any decent builder will be buying materials on account, on at least 14 days terms but more likely to be 28 days. The intervals you pay at is between you and your builder, it could be weekly or monthly. Generally operating under a terms of contract with staggared payments agreed on completion of task, can make it fair on boths sides.

I’d never ask for labour costs upfront, rather one a staged basis. I.e weekly or something. I’d only be discussing a deposit if there were materials to be ordered and paid beforehand

No, the only reason to pay 40% deposit is if the material costs are very high. In this event I would recommend buying the material yourself with the assistance/materials list from your contractor and have the material delivered to site. For a small £4000 job I would expect to pay a nominal retaining deposit if you must, then agree a payment schedule as milestones are achieved.

Normally 25% deposit upfront as a good will and balance on completion unless it is a job that is going to take more then 4 weeks then a £1,000 upfront and stage payments agreed by both parties I have used this system for the last thirty years and it works well for everyone