Hi Gazza,
You need to be aware that the criteria for claiming PIP and ESA are different, which is why there are 2 separate assessments. In particular, the ESA criteria is for mobility not walking. The assessor is allowed to decide that you could self-propel a wheelchair, even if you do not have one and have never been advised to do so. If you would not be able to self-propel then you must make this clear in order to satisfy the mobility descriptor. With this proviso in mind, it won't hurt to take the PIP letter with you.
Nothing on this board constitutes legal advice - always consult a professional about specific problems