How estimates will work

A Proposal would be a description of how you might answer a brief or query, it may or may not have any figure(s) attached. It may masquerade as an estimate, being essentially a list of items with a introduction/method.

An estimate would be an assessment of the cost of implementing your proposal based on current knowledge. It is generally understood in business to not be an offer, though often is read as such by consumers. You may expect it to vary according to conditions and new information on progress of the work, but note that naive clients might expect it to _not_ vary... If a contract is formed with just an estimate as the paperwork there is potentially more flexibility for the supplier, but a customer could push back on reasonability grounds if you were to try and stuff them, particularly if you should have reasonably been expected to have known about the extra costs and were misrepresenting the true cost.

A quote is generally considered a firm commitment to a final price and is an offer that can be accepted by the customer to form a legally binding contract (with that intention), and suppliers may find it difficult to negotiate an increase, unless the change were reasonable (extra work on uncovering dry rot in a building for instance, or clear increases in project scope, or identified customer generated delays etc.)

In most business, using the language above, the flow would be:

1) Query or Enquiry received
2) Proposal sent (generally with ballpark single headline figures)
3) Extra information received in response, with a request for a more detailed estimate
4) Estimate sent (level of cost detail increased, options included)
5) Request for a Quote received (identifying final selection of options)
6) Quote with number/identifier sent (including scope limitations and terms)
7) Numbered Purchase Order for Quote received (including terms etc.)
8) Work Done
9) Invoice against Purchase Order sent
10) Payment received

Forming a legally binding contract doesn't need any paperwork at all - just agreement/intention to enter into a legally binding contract, consideration and reasonability. If you shook on, said, wrote, estimated or quoted it would cost about or exactly £2000, were paid some or all of that, did most of the work and a week from finishing went back with a bill for £8000 there would be some sorting out to do...

Consumers have some statutory rights relating to reasonable cost, business customers need to take more precautions, as do suppliers. Should a contract be judged not to be in place for all or part of the work (It's £8000 because you did £6000 of 'extra' work which they refuse to pay for because "it wasn't in the quote" but YOU say they requested additions during the course of the work), it might mean looking at a Quantum Meruit claim for 'what the job is worth'. However, the sorting out the value of work done in a billing dispute, who asked for what when, and whether they thought/might reasonably have been expected to think you would bill them is a very big pain in the arse. Especially if the work stretches over a few months and you're scratching around for evidence of justification and instructions that were given.

Best pay attention to what you put in the paperwork and the expectations you are raising in the client throughout the progress of the work, don't let the bill creep up without recording assent along with the instruction... ( Delete or Edit)