Is this ptosis or something else? Please name what it could be if it's not ptosis.

Ptosis simply means a low upper eyelid, which you clearly have. However, you will need to be examined carefully to determine the cause for this. The treatment will depend of the cause but as a general rule, for a ptosis of this degree, you are likely to need some form of surgery, most probably a levator advancement procedure. It would probably be advisable to get the LASIK  don first as he speculums use can quite often make the ptosis worse.The cost will most likely be £3-5K, depending on the surgeon and the hospital.

Azu1,       It looks like from your pictures there may be some mild to moderate ptosis of the right eyelid.  This is something that can be treated surgically.  The cost for the surgery varies depending on region, and would also depend on the type of surgery needed (transconjunctival repair vs open).  A thorough exam with measurements and drops would be needed to accurately answer that question.  Also an in person consultation to evaluate for any other facial asymmetry would also be important.  Regarding the timing of surgery.  I would prioritize which is most important for you, but definitely recommend adequate recovery time between the surgeries, to prevent overexposing the cornea and poor healing.  You should consider consultation with both your plastic surgeon and lasik surgeon prior to getting either.  Good luck.