The vat has to be added somewhere on the supply chain.
The govt will take the vat either way…. But would they actually take it twice?
No, it won't get charged twice - at least not directly *.
As a non registered trader :
You buy the goods on which VAT is charged. You cannot reclaim this VAT so the cost to you is the VAT-inclusive price.
You do not add VAT on your labour.
So the cost to your client is "goods+VAT + labour". Because you are not registered, the VAT element is not recoverable anywhere.
The end result is that the materials cost your client 20% more *.
By allowing the client to buy the materials, they can reclaim the VAT, so they avoid that 20% markup.
If you were registered, then you reclaim the VAT on the materials so the cost to you is the ex-VAT price. When you invoice the client you charge VAT on the whole amount, which your client can reclaim. So nett, no VAT has been paid - it's just gone round the loop a couple of times !
* arguably, if you have paid VAT on materials which the client can't reclaim, there is double charging in that your client will charge VAT on the sales who's profits pay for those materials that VAT couldn't be reclaimed on.
For completeness, for a non-registered client is :
If you are not registered, the client pays VAT on the materials whether you buy them or the client does. There’s no VAT on your labour.
If you are registered, then you reclaim the VAT on materials, but charge VAT on the whole bill. So your labour costs the client 20% extra.
So, for non-registered clients (almost all domestic clients), it's better to be non-registered as your labour won't have a non-recoverable 20% markup.
For registered clients, there's a benefit to be registered OR let them buy the materials. Otherwise there's a non-recoverable 20% markup on materials.