Formation of a contract is the offer to do the work and then the acceptance of the offer. The third part, payment often comes later so is not relied upon as being necessary before the contract is formed but is essential for there to be something offered as payment.
So then comes the "intention to create the legal relations" (ie the contract) and this is not the actual payment, as the contracted works would have allready started by the time payment is made, so it is the actions taken by the parties with the intention of fulfilling the contract. Things like the OP getting a loan, tidying the garden ready for the builder, or booking time off work .... and for the builder, pencilling in the job, organising his labour and materials, measuring the site and such like.
These actions will demonstrate that the parties intended to fulfill their parts of the agreement after the offer/acceptance stage.
As for "If that isn’t true, then I could give you a quote for a large job for supplying and installing materials and you accept it, then I would be legally obliged to do the work and you could dictate the work schedule and how you were to make payments to me?"
What you are describing there are the contract terms, and not the actual contract service. So no, I could not dictate the work schedule or the payment terms, and neither could you dictate those to me as they were not agreed. The only thing agreed in this scenario is that you would supply and install the materials, and I would give you something for doing that.