IANAL, but the first step is to find whether you need planning permission for the work. Talk to your local council's planning department. They are usually helpful.
If you do need to submit a planning application, you will have to create drawings in a standard architectural format for inspection by anyone who may potentially be affected by the work - e.g. the owners of neighbouring properties. The planning department will notify them of the application to give them opportunity to comment on it before it is approved. 87
These drawings don't specify the technical details of the construction, but show the changes to the appearance of the existing buildings.
Whether you need planning permission or not, the work needs to comply with the UK building regulations.
See here for (detailed) official guidance on how to do that.
You may also want to contact the house insurers at the planning stage, rather than presenting them with a fait accompli at the end. They may wish to inspect the work in stages as it is carried out, or require copies of any planning department inspections. Failure to coordinate all the required inspections can cause significant delays to the work plan.
In general, the UK system doesn't care about the formal qualifications of the people involved, so long as the work meets the required standards. AFAIK there is no legal necessity for any form of insurance either on the work itself or the finished building - though it would be foolish not to have insurance against third party claims if there is any risk of a disaster damaging other people's property.
You will probably want some long-term guarantee of the work done should you want to sell the property - e.g. the National House-Building Council's standard guarantee is 10 years. That should be provided by the builder.
Since the builder will be guaranteeing the work, they will need to be satisfied that the technical specifications for the work are sensible, rather than just "doing whatever you tell them" regardless of the risks involved.
You may also require final inspections if you have made major changes to the water, gas, or electricity installations.
The bottom line of all this is that "doing the calculations" is often trivial compared with "understanding how the system works" - which is the expertise that professionals working in the field have. 87