It's 2 weeks from the date of request by your GP. It no longer remains a right if you choose to change the appointment, say you can't make it or ask for a different location as you are waiving your rights. If they could slide the 2 weeks back on the basis of them changing hospital it would allow the NHS to start massaging their lead times so I don't think that would be allowed (or at least it wouldn't once the media got a hold of it...bosses may certainly try such things until they are caught out
). However, from a practical point of view it may not be reasonable in certain circumstances e.g. the first hospital drops the ball and the second only has 48hrs to make the target, but certainly nothing like 6-8 weeks but it may be legally considered "as soon as is possible" which then becomes subjective (I've worked with lead times in regulatory environments in the utility sector and this tends to be how governance word any it to allow for later appraisal of whether the service have attempted to do as much as they can, but I can't speak for the NHS lead times). It may say in one of the above docs.
There are a load of NHS pledges on top of this that cover diagnosis and starting any treatment but they aren't legal rights.