Kens right I'm afraid Georgina, although you might be able to negotiate a cheap rate for them to do the job. The floor level inside will have been set in respect to the DPC level, so doing a chemical injection, may require remedial work to the lower part of the internal wall to reflect the raised external level.
If you were to install an surface drain around the conservatory, do you have a convenient place to run the drain into. You'd need someone with a diamond blade on a 9" angle grinder to cut a slot around the conservatory, and then cement the drain into place, so do you know someone that's reasonably competent to do the job.