Do I have to accept what a structural engineer draws as proposed loft conversion?

You cannot go against his Calculations as long as they have been checked by the Local Council Engineer and are Right. It seems as though there may be a difference in Design with your Neighbour. Ask your neighbour if you can see their design and Calculations. You cannot legally copy these Drawings or Calcs but You could then ask your Engineer to have a re-think and ask how much it would cost before he does it. Building Control are Rarely wrong. You could ask another Engineer but ask for a quote first.

There is no 'final' or 'absolute' solution when it comes to design. This would appear to be more of a contractual issue about what you and the engineer agreed on their appointment. It would be prudent to go back and check exactly what you instructed the engineer to do for you. If you have given them full authority to design the space as they see best then you may be stuck unless you wish to pay for a re-design or a second opinion. However, if you have instructed them to provide calculations for a design that closely resembles your neighbours or to make a pre-existing design (by an architect/technologist for instance) work, then you would be within your rights contractually to ask the engineer to either provide detailed reasoning why this was not possible, or to re-design the structure according to the design you gave them on appointment. If they have provided you an alternative design to one supplied as part of the brief, and you have not agreed to the alternative prior to the engineer carrying it out, you may not be liable to pay for the work done on this design. Keep in mind however, if you have not provided a detailed brief and the engineer's proposal is approved by Building Control, they have done nothing wrong. If you still feel the engineer is not carrying out their duties to the expected standard, you can raise a complaint with their regulatory and/or professional body as they can help to mediate cases of disagreement and mete out punishment where the engineer is not upholding their professional code of conduct.

Doing the same calculation twice should give the same answer. You need to change a different parameter of the design for the answer to change. What is the reason the space is smaller? Is it because the structural members need to be bigger than you anticipated, or is it because of other factors such as party wall issues or planning? There are usually many ways to skin a cat and this can also be the case with structural design. From your description your engineer sounds unwilling to look at alternatives, which of course will make it more difficult to find a more suitable option. If you ask your engineer to redo parts of the work then that should of course be cheaper than finding a new engineer to do it all over again.

Hi, a structural engineer is not an architect. Get an architect involved and the structural engineer will size the structural nembers to suit your requirements.

Different engineers work to different parameters based on their insurance and the safety factors they are required to include in their design. That said, it shouldn't make a large difference. It may be a case of including more steelwork to make the floor buildup slimmer (which I assume is causing the loss of space) but the offset is an increase in cost of steelwork and installation. If you asked for the cheapest solution, it sounds like this is what you got; if you asked for the solution which gave you the most useable space he may have returned a different design which cost more?